If √((1 − a2)(1 − b2)) = 3/5 and b = 2/5, evaluate: [(4a2 + 4b2 + 8ab) + (4a2 + 4b2 − 8ab)]
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Correct answer: A
Explanation
Given,
√((1 − a²)(1 − b²)) = 3/5, तथा b = 2/5
b² = 4/25
√((1 − a²) × 21/25) = 3/5
On squaring both sides,
(1 − a²) × 21/25 = 9/25
1 − a² = 9/21 = 3/7
a² = 4/7
(4a² + 4b² + 8ab) + (4a² + 4b² − 8ab) = 8a² + 8b²
= 8(4/7 + 4/25)
= 32(1/7 + 1/25)
= 32 × 32/175
= 1024/175