Question

if 1+1/x=3 find the value of x⁴+1/x⁴​​

Answer 1

Step-by-step explanation:

$1+\frac{1}{x}=3$

∴$\frac{x+1}{x}=3$

∴$x+1=3x$

∴$x-3x+1=0$

∴$-2x=-1$

∴$x=\frac{1}{2}$

so the value of$x^{4}+\frac{1}{x^{4} }$

is as followed

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

∴$\frac{1}{16}+\frac{1}{\frac{1}{16} }$

∴$\frac{1}{16} + 16$

on solving we get

$\frac{257}{16}$

Hope it helps