Question

if x - 1/x = 5 , find the values of x^2 + 1/x^2 and x ^4 +1 /x ^4
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Answer 1

Answer:

Now,

For first answer Steps

Squaring both sides will give

(x-1/x) ²=(5)²

x²+1/x²-2=25 Using (a-b) ²= a²-2ab+b²

x²+1/x²=27

Now for second answer

Again squaring both sides give

(x²+1/x²) ²= (27)²

x⁴+1/x⁴+2=729

x⁴+1/x⁴=727

Answer 2

$\Large\underline\mathbb\blue{ANSWER}$

$\tt{{x - \frac{1}{x} } } =5$

On squaring both sides,

$\tt{{({x - \frac{1}{x} })^{2} } } ={(5 ) }^{2} \\ \\ \implies \tt{ {(x)}^{2} + 2( \cancel{x})( \frac{1}{ \cancel{x}} ) - { (\frac{1}{x} )}^{2} } \\ \\ \implies \tt{ {x}^{2} - \frac{1}{ {x}^{2} } = 27 }$

$\tt{{( {x}^{2} - \frac{1}{ {x}^{2} }) }^{2} ={( 27) }^{2} } \\ \\ \implies \tt{ { {x}^{4} - \frac{1}{{x }^{4} }+ 2 = {(27)}^2 }} \\ \\ \implies \tt{ {x}^{4} - \frac{1}{{x }^{4} } = 729 - 2} \\ \\ \implies \tt{ \boxed{ \tt{ \pink{{x}^{4} - { \frac{1}{{x }^{4} }} = 727}}}}$

hope it's helpful ✅✅✅