Question

ifx+1/x=√5 find x^4+1/x^4

Answer 1

After Squaring both sides we get

x^2+ 1/x^2=3

Squaring once again we get

x^4+ 1/x^4=7

Answer 2

HEYA !

Given that,

$x + \frac{1}{x} = \sqrt{5}$
Squaring both sides , We get

${ \biggl(x + \frac{1}{x} \biggl)}^{2} = { (\sqrt{5} )}^{2} \\ \\ \Rightarrow \: \: {x}^{2} + \frac{1}{ {x}^{2} } + 2 \times x \times \frac{1}{x} = 5 \\ \\\Rightarrow \: \: {x}^{2} + \frac{1}{ {x}^{2} } + 2 = 5 \\ \\ \Rightarrow \: \:{x}^{2} + \frac{1}{ {x}^{2} } = 3$
Again Squaring both sides , We get

${ \biggl( {x}^{2}+ \frac{1}{ {x}^{2} } \biggl) }^{2} = {3}^{2} \\ \\ \Rightarrow \: \: {({x}^{2}) }^{2} + {\biggl( \frac{1}{ {x}^{2} } \biggl) }^{2} + 2 \times {x}^{2} \times \frac{1}{ {x}^{2} } = 9 \\ \\ \Rightarrow \: \: {x}^{4} + \frac{1}{ {x}^{4} } + 2 = 9 \\ \\ \Rightarrow \: \: \boxed{ \: {x}^{4} + \frac{1}{ {x}^{4} } = 7 \: }$

$\mathbf{HOPE \: \: \: IT \: \: \: HELPS }$