Question

if x =1/x-5 find x-1/x x+1/x x^2 + 1/x^2

Answer 1

given , x = 1 /x - 5


x - 1 / x = - 5


squaring both sides , we get



( x - 1 / x )^2 = ( - 5) ^2



x^2 + 1 / x^2 - 2( x ) ( 1/ x) = 25




x^2 + 1/ x^2 - 2 = 25



x^2 + 1/ x^2 = 27


( x)^2 + ( 1/ x )^2 + 2 ( x ) ( 1 /x ) - 2 (x ) (1 /x) = 27




( x + 1 / x )^2 - 2 = 27




( x + 1 /x )^2 = 29







( x + 1 / x ) = √29


hence value of ( x - 1 / x ) = - 5 ,

( x + 1 /x ) = √29



x^2 + 1/ x^2 = 27
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【 hope helps 】
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