SarkariPYQ

SSC Selection Post 2019 PYQ — Question 65

SSC Selection Post - Matriculation Level 2019 - 15 Oct 2019 • Quantitative Aptitude • Q65

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If 27 (x+y)3 + (x - y)3 = 2(2x+y) (Ax² + Bxy+Cy²), then what is the value of (A-B+C)?

 

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Correct answer: C

Explanation

The correct answer is Option 3 i.e. 4

LHS :

27(x+y)3=27(x3+3x2y+3xy2+y3)27(x + y)^3 = 27(x^3 + 3x^2y + 3xy^2 + y^3)

(x−y)3=x3−3x2y+3xy2−y3(x - y)^3 = x^3 - 3x^2y + 3xy^2 - y^3

Add: =28x3+78x2y+84xy2+26y3= 28x^3 + 78x^2y + 84xy^2 + 26y^3

RHS :

2(2x+y)(Ax2+Bxy+Cy2)=4Ax3+2(2B+A)x2y+2(2C+B)xy2+2Cy32(2x + y)(Ax^2 + Bxy + Cy^2) = 4Ax^3 + 2(2B + A)x^2y + 2(2C + B)xy^2 + 2C y^3

Match coefficients:

4A = 28 ⇒A =7 

2(2B + A) = 78 ⇒ B =16 

2(2C + B) = 84 ⇒ C = 13

A - B + C = 7 - 16 + 13 = 4