If x + (1/x) = 8, then find the value of x³ + (1/x³) _____?
- 488
- 512
- 500
- None of these
Explanation
Given:
x + (1/x) = 8
Cube both sides:
(x + (1/x))³ = 8³
Expand the left side:
x³ + 3x²(1/x) + 3x(1/x)² + (1/x)³ = 512
Simplify:
x³ + 3x + 3(1/x) + (1/x)³ = 512
Rearrange:
x³ + (1/x)³ + 3(x + (1/x)) = 512
Substitute x + (1/x) = 8:
x³ + (1/x)³ + 3(8) = 512
x³ + (1/x)³ + 24 = 512
Subtract 24 from both sides:
x³ + (1/x)³ = 488
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اس سوال کو وضاحت کے ساتھ پڑھیں
- (t² + 4)(t - 2)(t - 2)
- (t² - 4)(t² - 4)
- (t² + 4)(t + 2)(t - 2)
- None of these
اس سوال کو وضاحت کے ساتھ پڑھیں
- +4
- -4
- +16
- None of these
اس سوال کو وضاحت کے ساتھ پڑھیں
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