GATE (GA) Textile 2018 Question Paper Solution | GATE/2018/GA/09

Question 09 (General Aptitude)

If $x^{2}+x-1=0$ , what is the value of $x^{4}+\frac{1}{x^4}$ ?

(A)	1
(B)	5
(C)	7
(D)	9

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$x^{2}+x-1=0$
Both side devide by x
$x+1-\frac{1}{x}=0$
$x-\frac{1}{x}=-1$
Square both side-
$(x-\frac{1}{x})^2=(-1)^2$
$x^2+\frac{1}{x^2}-2=1$
$x^2+\frac{1}{x^2}=3$
Again square both side-
$x^4+\frac{1}{x^4}+2=9$
$x^4+\frac{1}{x^4}=7$ (Ans)

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