Question

x-1/x=2 then X4+1/X4=?

Answer 1

Hi...☺
Here is your answer...✌
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Given that,
$x - \frac{1}{x} = 2 \\ \\ Squaring \: both \: sides \: \\ we \: get ,\\ \\(x - \frac{1}{x}) {}^{2} = 2 {}^{2} \\ \\ {x}^{2} + \frac{1}{x {}^{2} } - 2 \times x \times \frac{1}{x} = 4 \\ \\ {x}^{2} + \frac{1}{x {}^{2} } - 2 = 4 \\ \\ {x}^{2} + \frac{1}{x {}^{2} } = 6\\ \\ Again, \: squaring \: both \: sides \\ we \: get ,\\ \\ {x}^{4} + \frac{1}{ {x}^{4} } + 2 \times x {}^{2} \times \frac{1}{x {}^{2} } = {6}^{2} \\ \\ {x}^{4} + \frac{1}{ {x}^{4} } + 2 = 36 \\ \\ {x}^{4} + \frac{1}{ {x}^{4} } = 34$

Answer 2

HELLO DEAR,

(x - 1/x) = 2

[ on SQUARING both side]

we get,

=> x² + 1/x² - 2×x×1/x = 4

=> x² + 1/x² = 4 +2

=> (x² + 1/x²) = 6

[again squaring on both side]

we get,


x⁴ + 1/x⁴ + 2×x² ×1/x² = 6²

=> (x⁴ + 1/x⁴) = 36 - 2

=> (x⁴ + 1/x⁴) = 34



I HOPE ITS HELP YOU DEAR,
THANKS