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If x = 4√15 , the value of x + √20 + x + √12 is √5 + √3 x − √20 x − √12
-
- 1
- 2
- √3
- √5
Correct Option: B
| x = | |
| √5 + √3 |
| = | |
| (√5 + √3)(√5 − √3) |
| = | |
| 5 − 3 |
= 2√15(√5 − √3) = 10√3 − 6√5
| ∴ | + | ||
| x − √20 | x − √12 |
| = | + | ||
| 10√3 − 6√5 − 2√5 | 10√3 − 6√5 − 2√3 |
| = | + | ||
| 10√3 − 8√5 | 8√3 − 6√5 |
| = | + | ||
| 5√3 − 4√5 | 4√3 − 3√5 |
| = | |
| (5√3 − 4√5)(4√3 − 3√5) |
| = | |
| 60 − 15√15 − 16√15 + 60 |
| = | |
| 120 − 31√15 |
| = | = 2 | |
| 120 − 31√15 |
