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If x + 1 = a and 1 − y = b , then the value of x − y is equal to x − 1 b 1 + y a 1 + xy
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2ab a2 − b2 -
a2 − b2 2ab -
a2 + b2 2ab -
a2 − b2 ab
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Correct Option: A
| = | ||
| x − 1 | b |
By componendo and dividendo,
| = | ||
| x + 1 − x + 1 | a − b |
| ⇒ | = | ||
| 2 | a − b |
| ⇒ x = | |
| a − b |
Again,
| = | ||
| 1 + y | a |
| ⇒ | = | ||
| 1 − y | b |
| ⇒ | = | ||
| 1 + y − 1 + y | a − b |
| ⇒ | = | ||
| 2y | a − b |
| ⇒ y = | |
| a + b |
| ∴ x − y = | − | ||
| a − b | a + b |
| = | = | ||
| (a + b)(a − b) | a2 − b2 |
| xy = | × | = 1 | ||
| a − b | a + b |
∴ Expression
| = | = | |||||
| 1 + xy | ||||||
| 1 + 1 |
| = | = | ||
| 2(a2 − b2) | a2 − b2 |
