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3 cho a,b,c > 0 và \(a^2b^2c^2=3\) C/m \(\dfrac{a^3}{bc}\dfrac{b^3}{ca}\dfrac{c^3}{ab} {a^3}{a^2b^2}\dfrac{b^3}{b^2c^2}\dfrac{c^3}{c^2a^2}>=\dfrac{abc}{2}\) Theo dõi Vi phạm YOMEDIA Toán 10 Chương 4 Bài 1 Trắc nghiệm Toán 10 Chương 4 Bài 1 Giải bài tập Toán 10 Chương 4 Bài 1 Trả lời (1) Bài 3Click here👆to get an answer to your question ️ Simplify (a^2b^2)^3(b^2c^2)^3(c^2a^2)^3/(a b)^3(bc)^3(ca)^3Consider a triangle with sides of length a, b, c, where θ is the measurement of the angle opposite the side of length cThis triangle can be placed on the Cartesian coordinate system aligned with edge a with origin at C, by plotting the components of the 3 points of the triangle as shown in Fig 4 = (⁡, ⁡), = (,), = (,) By the distance formula, = (− ⁡) (− ⁡)

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(a^2-b^2)^3+(b^2-c^2)^3+(c^2-a^2)^3/(a-b)^3+(b-c)^3+(c-a)^3-(abc) 2 =a 2 b 2 c 2 2ab2bc2ca for abbcca ≤ a 2 b 2 c 2 I got 3ab3bc3ca ≤ a 2 b 2 c 2 2ab2bc2ca so 3(abbcca) ≤ (abc) 2 is there something wrong?3 cho a,b,c > 0 và \(a^2b^2c^2=3\) C/m \(\dfrac{a^3}{bc}\dfrac{b^3}{ca}\dfrac{c^3}{ab} {a^3}{a^2b^2}\dfrac{b^3}{b^2c^2}\dfrac{c^3}{c^2a^2}>=\dfrac{abc}{2}\) Theo dõi Vi phạm YOMEDIA Toán 10 Chương 4 Bài 1 Trắc nghiệm Toán 10 Chương 4 Bài 1 Giải bài tập Toán 10 Chương 4 Bài 1 Trả lời (1) Bài 3

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S Subhotosh Khan Super Moderator (a 3 b 3 c 3)(1/a1/b1/c) ≥(abc) 2 Now, the LHS = (a 3 b 3 c 3)(1/a1/b1/c) = (sqrt1)a b c^2 = a^2 b^2 c^2 2*ab bc ca 2)a^3 b^3 c^3 3abc = (abc)(a^2 b^2 c^2 ab bc ca) Using 1st note 1^2 = 2 2*ab bc ca so ab bc ca = 1/2 (Memorize this as Equation 2) Using 2nd formula in NOTE1)a b c^2 = a^2 b^2 c^2 2*ab bc ca 2)a^3 b^3 c^3 3abc = (abc)(a^2 b^2 c^2 ab bc ca) Using 1st note 1^2 = 2 2*ab bc ca so ab bc ca = 1/2 (Memorize this as Equation 2) Using 2nd formula in NOTE

As stated in the title, I'm supposed to show that $(abc)^3 = a^3 b^3 c^3 (abc)(abacbc)$ My reasoning $$(a b c)^3 = (a b) c^3 = (a b)^3 3(a b)^2c 3(a b)c^2 c^3 Stack Exchange network consists of 176 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careersABC with 3 replicates (1,2,3) and two factors, eg D E as random effects) I am interested in discussing the main effects (A,B,C) and their interactions between these main effects on theFree PreAlgebra, Algebra, Trigonometry, Calculus, Geometry, Statistics and Chemistry calculators stepbystep

4 Rs 1 are divided among A, B, C such that A's share is Rs more than B's and Rs less than C's What is B's shareGroup 1 (ac) • (a 2 c 2) Group 2 (ab) • (a 2 b 2) Group 3 (bc) • (b 2 c 2) Looking for common subexpressions Group 1 (ac) • (a 2 c 2) Group 3 (bc) • (b 2 c 2) Group 2 (ab) • (a 2 b 2) Bad news !!Đề bài của bạn bị nhầm Nếu đúng như dấu bằng xảy ra thì phải là CMR \(3(a^3b^3c^3)\geq a^2b^2c^2\) Lời giải

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Let c be chosen to be the longest of the three sides and a b > c (otherwise there is no triangle according to the triangle inequality) The following statements apply If a 2 b 2 = c 2, then the triangle is right If a 2 b 2 > c 2, then the triangle is acute If a 2 b 2 < c 2, then the triangle is obtuseDefinition The longest side of the triangle is called the "hypotenuse", so the formal definition is\(\frac{(a^2b^2)^3(b^2c^2)^3 (c^2a^2)^3}{(ab)^3(bc)^3(ca)^3}\) on simplification is equal to a) (c) (a b) (b c) (c a) (d) 0 Welcome to Sarthaks eConnect A unique platform where students can interact with teachers/experts/students to get solutions to their queries

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The sides AB, BC, CD and DA of a quadrilateral have the equations x 2y = 3, x = 1, x 3y = 4, 5x y 12 = 0 asked Dec 31, 18 in Mathematics by kajalk ( 777k points) straight lines0 (0) Upvote (0) Choose An Option That Best Describes Your Problem Answer not in Detail Incomplete Answer Answer Incorrect Others Thank you Your Feedback will Help us Serve you better`3(a^4b^2a^2c^4a^4c^2b^4c^2a^2b^4b^2c^4)` If you rearange the terms in the last factor you will see that they are identical to the result we got form multiplying the left hand side, hence

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(c) a statement giving any available information respecting the identification, location, income and assets of the respondent Idem (4) On receipt of the documents referred to in subsection (3), the Attorney General shall send the documents to the Attorney General for the province in which the respondent is ordinarily resident Further evidenceNow we will learn to expand the square of a trinomial (a b c) Let (b c) = x Then (a b c) 2 = (a x) 2 = a 2 2ax x 2 = a 2 2a (b c) (b c) 2 = aMatha^2b^2c^2\frac 1 {a^2}\frac 1 {b^2}\frac 1 {c^2}=6/math matha^2\frac 1 {a^2}2b^2\frac 1 {b^2}2c^2\frac 1 {c^2}2=0/math math(a\frac 1 a)^2

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Factoring by pulling out fails The groups have no common factor and can not be added up to form a multiplication FinalThe answer is 2^3*3^2*5^1*103*107 as this is a multiple of 12, Now 1284 and 2472 are multiples of that number So HCF of these three is HCF of 1284 and 2472 which is 12 Verify using def GCD(a,b)(a^2b^2)^3 (b^2c^2)^3 (c^2a^2)^3 divided by(ab)^3 (bc)^3 (ca)^3 Math Polynomials

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(a^2b^2)^3 (b^2c^2)^3 (c^2a^2)^3 divided by(ab)^3 (bc)^3 (ca)^3 Math Polynomials31 b 2 raised to the 2 nd power = b ( 2 * 2 ) = b 4 32 c 3 raised to the 2 nd power = c ( 3 * 2 ) = c 6 Equation at the end of step 3 2 2 a 2 b 4 a 6 c 3 —————— • ———— c 6 b 3 Step 4 Multiplying exponential expressions 41 a 2 multiplied by a 6 = a (2 6) = a 8 Dividing exponential expressions 42 b 4 dividedWhat must be subtracted from the polynomial x 3 1 3 x 2 3 5 x 2 5 so that the resulting polynomials is exactly divisible by x 2 1 1 x 1 0 View solution Divide

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$\frac{a^3}{a^2abb^2}\frac{b^3}{b^2bcc^2}\frac{c^3}{c^2caa^2}\geq \frac{abc}{3}$ posted in Bất đẳng thức và cực trị Cho a, b, c là các số thực dương thỏa mãn $\frac{a^3}{a^2abb^2}\frac{b^3}{b^2bcc^2}\frac{c^3}{c^2caa^2}\geq \frac{abc}{3}$ Để giải bài này ta chứng minh $\frac{a^3}{a^2abb^2}\geq \frac{2ab}{3}$ (Tương đương $(ab)(a$$ \begin{align*} \sum\limits_{a,b,c} a^3 &\geq \sum\limits_{a,b,c} a^2b\\ \sum\limits_{a,b,c} a &\geq \sum\limits_{a,b,c} b\\ abc &\geq abc \end{align*} $$ Which is true, but it would imply that equality always holds, which is obviously false So why can't I just divide in a cycling sum?If a,b,c are all nonzero and a b c = 0, prove that a2/bc b2/ca c2/ab = 3 asked Sep 14, 18 in Class IX Maths by aditya23 ( 2,139 points) polynomials

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Transcript Example 3 Let A = {1, 2, 3}, B = {3, 4} and C = {4, 5, 6} Find A × (B ∩ C) B ∩ C = {3, 4} ∩ {"4, 5, 6" } = {"4" } A × (B ∩ C) = {"1, 2, 3Example Solve 8a 3 27b 3 125c 3 – 90abc Solution This proceeds as Given polynomial (8a 3 27b 3 125c 3 – 90abc) can be written as (2a) 3 (3b) 3 (5c) 3 – 3(2a)(3b)(5c) And this represents identity a 3 b 3 c 3 3abc = (a b c)(a 2 b 2 c 2 ab bc ca) Where a = 2a, b = 3b and c = 5c Now apply values of a, b and c on the LHS of identity ie a 3 b 3 c 3(a^2b^2)^3 (b^2c^2)^3 (c^2a^2)^3 divided by(ab)^3 (bc)^3 (ca)^3 Math Polynomials

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It is called "Pythagoras' Theorem" and can be written in one short equation a 2 b 2 = c 2 Note c is the longest side of the triangle;S Subhotosh Khan Super Moderator (a 3 b 3 c 3)(1/a1/b1/c) ≥(abc) 2 Now, the LHS = (a 3 b 3 c 3)(1/a1/b1/c) = (sqrtFree PreAlgebra, Algebra, Trigonometry, Calculus, Geometry, Statistics and Chemistry calculators stepbystep

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Factorization is (c a) • (c a) Equation at the end of step 1 ((((a 2)(b 2))•3)(((b 2)(c 2))•3))3•(ac)•(ca) Step 2 Trying to factor as a Difference of Squares 21 Factoring b 2c 2 Check b 2 is the square of b 1 Check c 2 is the square of c 1 Factorization is (b c) • (b c)It is called "Pythagoras' Theorem" and can be written in one short equation a 2 b 2 = c 2 Note c is the longest side of the triangle;Hence a 3 b 3c 3 − 3abc = (a b c)(a 2 b 2 c 2 ab – bc ca) Was this answer helpful?

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3(abc)² 3(234)² 3(9)² 3(81) = 243 If the "2" is not an exponent, then 3(abc)2 3(234)2 3(10)2 3() = 60 Next time please further elaborate whether the "2" is an exponent or a number Best of luck, JessieTo ask Unlimited Maths doubts download Doubtnut from https//googl/9WZjCW If `abc=6`, `a^2b^2c^2=14` & ` a^3b^3c^3=36` , find `abc`2g=12(32g1)11 One solution was found g = 1/3 = 0003 Rearrange Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation

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(a b c) 2 = a 2 b 2 c 2 2ab 2bc 2ca (a (−b) (−c)) a 3 b 3 c 3 − 3abc = (a b c) (a 2 b 2 c 2 − ab − bc − ac) If (a b c) = 0, a 3 b 3 c 3 = 3abc Some not so Common Formulas Power n Formula a n − b nDefinition The longest side of the triangle is called the "hypotenuse", so the formal definition isIt is called "Pythagoras' Theorem" and can be written in one short equation a 2 b 2 = c 2 Note c is the longest side of the triangle;

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Definition The longest side of the triangle is called the "hypotenuse", so the formal definition isSolve your math problems using our free math solver with stepbystep solutions Our math solver supports basic math, prealgebra, algebra, trigonometry, calculus and moreThe sides AB, BC, CD and DA of a quadrilateral have the equations x 2y = 3, x = 1, x 3y = 4, 5x y 12 = 0 asked Dec 31, 18 in Mathematics by kajalk ( 777k points) straight lines

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Solve your math problems using our free math solver with stepbystep solutions Our math solver supports basic math, prealgebra, algebra, trigonometry, calculus and moreA and b are the other two sides ;(abc) 2 =a 2 b 2 c 2 2ab2bc2ca for abbcca ≤ a 2 b 2 c 2 I got 3ab3bc3ca ≤ a 2 b 2 c 2 2ab2bc2ca so 3(abbcca) ≤ (abc) 2 is there something wrong?

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You may file Forms W2 and W3 electronically on the SSA's Employer W2 Filing Instructions and Information web page, which is also accessible at Copies B, C, and 2 and ask your employer to correct your employment record Be sure to ask the employer to file Form W2c, Corrected Wage and Tax Statement, with the SocialA^3 b^3 c^3 3abc = (a b c)(a^2 b^2 c^2 ab ac bc) By assumption a^3b^3c^3=3abc so the left hand side is 0 Therefore (abc)(a^2b^2c^2abacbc) = 0 So either abc=0 or a^2b^2c^2abacbc=0 Now suppose a^2b^2c^2 abacbc =0 You can rewrite this as (1/2) ( (ab)^2 (bc)^2 (ca)^2 )=0A and b are the other two sides ;

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A and b are the other two sides ;4 a 2 1 2 a b 9 b 2 − c 2 ( 2 a 3 b c ) ( 2 a 3 b c ) = (2 a 3 bNotice that #(AB)^3(BC)^3(CA)^3# #=(color(red)(cancel(color(black)(A^3)))3A^2AB^2color(red)(cancel(color(black)(B^3))))(color(red)(cancel(color(black)(B^3

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Factor (a^2b^2)^3(b^2c^2)^3(c^2a^2)^3 Use the Binomial Theorem Simplify each term Tap for more steps Multiply the exponents in Tap for more steps Apply the power rule and multiply exponents, Multiply by Rewrite using the commutative property of multiplication Multiply by0 (0) Upvote (0) Choose An Option That Best Describes Your Problem Answer not in Detail Incomplete Answer Answer Incorrect Others Thank you Your Feedback will Help us Serve you better여기까지가 중학교 과정이다 15 개정 교육과정 기준으로 중학교 3학년 1학기 과정에 나온다 2 09 개정 교육과정에서는 2학년 1학기 과정에서 이 공식들을 배웠으나, 이번에 인수분해와 함께 연계시키기 위해서 3학년으로 올린 듯 3 이 아래부터는 고등 수학 (상)에서 배우게 된다

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