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If a = √6 + √5 , b = √6 − √5 then 2a2 – 5 ab + 2b2 = ?
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- 38
- 39
- 40
- 41
Correct Option: B
a = √6 + √5 , b = √6 − √5
a − b = √6 + √5 − √6 + √5 = 2√5
ab = (√6 + √5)(√6 − √5)
= 6 – 5 = 1
∴ 2a2 – 5ab + 2b2
| = 2 |  | a2 − | ab + b2 |  | |
| 2 |
| = 2 | | a2 − 2ab + b2 − | ab | | |
| 2 |
= 2 (a2 – 2ab + b2) – ab
= 2 (a – b)2 – ab
= 2 × (2√5)2 − 1
= 2 × 4 × 5 – 1 = 40 – 1 = 39
