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SSC CGL 2020 PYQ — Question 62

SSC CGL - 4th March 2020 Shift 3 • Quantitative Aptitude • Q62

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If 2x2 + y2 + 8z2 - 2√(2yz) + 4√(2yz) - 8zx = (Ax + y + Bz)2, then the value of (A2 + B2 - AB) is:

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Correct answer: C

Explanation

The correct answer is Option 3 i.e 14.

Understanding/Application

2x2 + y2 + 8z2 - 2√(2yz) + 4√(2yz) - 8zx = (Ax + y + Bz)2

(- √2x)2 + y2 + (2√2z)2 + 2(-√2x)(y) + 2y(2√2z) + 2(-√2x)(2√2z) = (Ax + y + Bz)2

(-√2x + y + 2√2z)2 = (Ax + y + Bz)2

A = - √2 

B = 2√2

(A2 + B2 - AB)

= {(-√2)2 + (2√2)2 - (-√2 × 2√2)}

= (2 + 8 + 4)

= 14