Question 75

If $$x^4 + x^{-4} = 194, x > 0$$, then the value of $$(x - 2)^2$$ is:

Solution

$$x^4 + x^{-4} = 194$$

$$(x^2 + x^{-2}) ^2$$= $$x^4 + x^{-4}$$ + 2 = 194 + 2 = 196

$$(x^2 + x^{-2})$$ =14

$$(x+ x^{-1}) ^2$$ = $$(x^2 + x^{-2})$$ +2 =14 + 2 =16

$$x+ x^{-1}$$ = 4

$$x^{2}$$ -4x +1 =0

$$(x - 2)^{2}$$ = $$x^{2}$$ -4x +4 = $$x^{2}$$ -4x +1 + 3 = 0 + 3 =3

So , the answer would be Option d)3.

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