If x2 + 1/x2 = 98 (x > 0), then the value of x3 + 1/x3 is:
Show answer & explanation
Correct answer: A
Explanation
The correct answer is Option 1 i.e. 970
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Understanding |
Application |
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Given: x2 + 1/x2 = 98 (x > 0) We know: (a + b)2 = a2 + b2 + 2ab and (a + b)3 = a3 + b3 + 3ab(a + b) |
So, (x + 1/x)2 = x2 + 1/x2 + 2 ⇒ (x + 1/x)2 = 98 + 2 ⇒ (x + 1/x)2 = 100 ⇒ (x + 1/x) = 10 Cubing both sides, (x + 1/x)3 = 103 x3 + 1/x3 = 103 - 3 × 10 = 970 |