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If a = √5 + 1 and b = √5 − 1 , then the value of √5 − 1 √5 − 1 a2 + ab + b2 is a2 − ab + b2
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3 4 -
4 3 -
3 5 -
5 3
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Correct Option: B
| a = | = | × | |||
| √5 − 1 | √5 − 1 | √5 + 1 |
| = | = | ||
| 5 − 1 | 4 |
| = | |
| 2 |
| ∴ b = | = | ||
| 2 | 2 |
| ∴ a + b = | + | = 3 | ||
| 2 | 2 |
| and ab = | × | = 1 | ||
| √5 − 1 | √5 + 1 |
| ∴ Expression = | = | ||
| a2 − ab + b2 | (a + b)2 − 3ab |
| = | = | = | |||
| 9 − 3 | 6 | 3 |
