Question

please see the given attachment

Answer 1

1) (x+1/x)²=(6)²
x²+1/x²+2(x)(1/x)=36
x²+1/x²+2=36
x²+1/x²=36-2
x²+1/x²=34

2) (x+1/x)⁴=(x²+1/x²)²=(34)²
x⁴+1/x⁴+2(x²)(1/x²)=1156
x⁴+1/x⁴+2=1156
x⁴+1/x⁴=1156-2
x⁴+1/x⁴=1154

hope it helps you....

Answer 2

1)

$x + \frac{1}{x} = 6$

Squaring both sides;

${(x + \frac{1}{x} )}^{2} = {6}^{2}$

${x}^{2} + 2 + \frac{1}{ {x}^{2} } = 36$

${x}^{2} + \frac{1}{ {x}^{2} } = 36 - 2$

Hence,

${x }^{2} + \frac{1}{ {x}^{2} } = 34$

2) first prove the above answer and the start....

Squaring both the sides;

${( {x}^{2} + \frac{1}{ {x}^{2} }) }^{2} = {34}^{2}$

${x}^{4} + 2 + \frac{1}{ {x}^{4} } = 1156$

${x}^{4} + \frac{1}{ {x}^{4} } = 1156 - 2$

Hence,

${x}^{4} + \frac{1}{ {x}^{4} } = 1154$

Hope it helps;

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