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If x = √5 + 1 and y = √5 − 1 , then the value of x2 + xy + y2 is √5 − 1 √5 + 1 x2 − xy + y2
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3 4 -
4 3 -
3 5 -
5 3
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Correct Option: B
| x = | |
| √5 − 1 |
| = | |
| (√5 − 1)(√5 + 1) |
(Rationalising the denominator)
| = | |
| 5 − 1 |
| = | |
| 4 |
| = | |
| 2 |
| ∴ y = | = | ||
| √5 + 1 | 2 |
| ∴ x + y = | + | ||
| 2 | 2 |
| = | = 3 | |
| 2 |
| xy = | × | ||
| 2 | 2 |
| = | = 1 | |
| 4 |
| ∴ | = | ||
| x2 − xy + y2 | (x + y)2 − 3xy |
| = | = | = | = | ||||
| (3)2 − 3 | 9 − 3 | 6 | 3 |
