If (4x + 2y)3 + (4x - 2y)3 = 16(Ax3 + Bxy2), then what is the value of 1/2(√A2 + B2)?
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Correct answer: B
Explanation
The correct answer is option 2 i.e. 5
(4x + 2y)3 + (4x - 2y)3 = 16 (Ax3 + Bxy2) .....(1)
a3 + b3 = (a + b)(a2 + b2 - ab)
(a + b)2 + (a - b)2 = 2(a2 + b2)
a2 - b2 = (a + b)(a - b)
(4x + 2y)3 + (4x - 2y)3 = (4x + 2y + 4x - 2y)[(4x + 2y)2 + (4x - 2y)2 - (4x + 2y)(4x - 2y)]
(4x + 2y)3 + (4x - 2y)3 = 8x[2(16x2 + 4y2)] - (16x2 - 4y2)
(4x + 2y)3 + (4x - 2y)3 = 8x(32x2 + 8y2 - 16x2 + 4y2)
(4x + 2y)3 + (4x - 2y)3 = 8x(16x2 + 12y2)
(4x + 2y)3 + (4x - 2y)3 = 16(8x3 + 6xy2) .....(2)
Checking equations (1 and (2 -
A = 8 and B = 6
(1/2)√(A2 + B2) = (1/2)√(82 + 62) = (1/2)√(64 + 36) = (1/2)√100 = 1/2 × 10 = 5