Question

if x-1/x=4 then evaluate x power 4 1/x power4​

Answer 1

Given:-

if x-1/x=4 then evaluate x power 4 1/x power4

Find:-

x power 4 1/x power4??

Solution:-

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: x + \frac{1}{x} = 2 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: (1)$

$\Big(x + \frac{1}{x} \Big) {}^{2} = 2 {}^{2}$

$x {}^{2} + \frac{1}{x {}^{2} } + 2 = 4$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: x {}^{2} + \frac{1}{x {}^{2} } = 2 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: (2)$

$\Big(x - \frac{1}{x} \Big) {}^{2} = x {}^{2} + \frac{1}{x {}^{2} } - 2 = 2 - 2 = 0$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: x - \frac{1}{x} = 0 \: \: \: \: \: \: \: \: \: (3)$

$(1) \times (3) = >$

$\Big(x + \frac{1}{x} \Big) \Big(x - \frac{1}{x} \Big) = 2 \times 0$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: x {}^{2} - \frac{1}{x {}^{2} } = 0 \: \: \: \: \: \: \: \: \: \: \: \: \: \: (4)$

$(2) \times (4) = >$

$\Big(x {}^{2} + \frac{1}{x {}^{2} } \Big) \Big(x {}^{2} - \frac{1}{x {}^{2} } \Big) = 2 \times 0$

$x {}^{4} - \frac{1}{x {}^{4} } = 0$