If x + (1/x) = 5, x ≠ 0, then the value of (x4 + 1/x2)/(x2 - 3x + 1) is equal to:
Show answer & explanation
Correct answer: D
Explanation
The correct answer is Option 4 i.e. 55.
| Understanding/Application |
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x + 1/x = 5 (x4 + 1/x2)/(x2 - 3x + 1) = [x(x3 + 1/x3)]/[x(x - 3 + 1/x)] |
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= (x3 + 1/x3)/(x - 3 + 1/x) = [(x + 1/x)3 - 3(x + 1/x)]/5 - 3 = (125 - 15)/2 = 110/2 = 55 |