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If a (x + y) = b(x – y) = 2ab, then the value of 2 (x2 + y2) is :
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- 2 (a2 − b2)
- 2 (a2 + b2)
- 4 (a2 − b2)
- 4 (a2 + b2)
Correct Option: D
a (x + y) = b (x – y)
⇒ ax – bx = – by – ay
⇒ bx – ax = ay + by
⇒ x (b – a) = y (a + b)
| ⇒ | = | ||
| a + b | b − a |
| = | = | ||
| (a + b)2(b − a)2 | 2(a2 + b2) |
∴ 2(x2 + y2) = 4(a2 + b2)
