Question

If (x-1/x)=4, find the value of
(i) (x^2+1/x^2)
(ii) (x^4+1x^4)​

Answer 1

Answer:

1. 18
2. 322

Step-by-step explanation:

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

By adding 2 on both sides, we get :

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

$(x^2+\frac{1}{x^2} )^2=x^4+\frac{1}{x^4} +2$ --- Identity 2

By subtracting 2 on both sides, we get :

$(x^2+\frac{1}{x^2} )^2-2=x^4+\frac{1}{x^4}$ --- 2'

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

$x^2+\frac{1}{x^2}=(4)^2+2$ *From 1'

∴ $x^2+\frac{1}{x^2}=18$

(ii) $x^4+\frac{1}{x^4}$

$x^4+\frac{1}{x^4}=(18)^2-2$ *From 2'

∴ $x^4+\frac{1}{x^4}=322$

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