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If x = √5 − √3 and y = √5 + √3 then the value of x2 + xy + y2 = ? √5 + √3 √5 − √3 x2 − xy + y2
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63 61 -
67 65 -
65 63 -
69 67
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Correct Option: A
| x = | , y = | ||
| √5 + √3 | √5 − √3 |
| ∴ x + y = | + | ||
| √5 + √3 | √5 − √3 |
| = | |
| (√5 + √3) × (√5 − √3) |
| = | |
| 5 − 3 |
= 5 + 3 = 8
| xy = | × | = 1 | ||
| √5 + √3 | √5 − √3 |
| = | |
| x2 − xy + y2 |
| ∴ | |
| (x + y)2 − 3xy |
| = | |
| (8)2 − 3 |
| = | |
| 64 − 3 |
| = | |
| 61 |
