If a3 = 117 + b3 and a = 3 + b, then the value of a + b is :
Show answer & explanation
Correct answer: A
Explanation
The correct answer is Option 1 i.e ±7
| Application |
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a3 – b3 = 117; a – b = 3 (a – b)(a2 + ab + b2) = 117 3 × (a2 + ab + b2) = 117 = a2 + ab + b2 = (117/3) = 39 (a - b)2 + 3ab = 39 32 + 3ab = 39 3ab = 39 – 9 = 30 ab = (30/3) = 10. (a + b)2 = (a - b)2 + 4ab = 9 + 4 × 10 = 49 a + b = √49 = ± 7 |