solve-x-2-3-2-x-3-

Question Number 174269 by mr W last updated on 28/Jul/22

s o l v e {(x^{2} - 3)}^{2} = x + 3

Answered by Frix last updated on 28/Jul/22

obviously x = 1 \lor x = - 2 the other 2 are easy

Answered by mr W last updated on 28/Jul/22

{(x^{2} - 3)}^{2} - 3 = x

l e t x^{2} - 3 = t \dots (i)

\Rightarrow t^{2} - 3 = x \dots (i i)

(i) - (i i) :

x^{2} - t^{2} = t - x

(t - x) (t + x + 1) = 0

\Rightarrow t - x = 0

\Rightarrow x^{2} - x - 3 = 0

\Rightarrow x = \frac{1 \pm \sqrt{13}}{2}

\Rightarrow t + x + 1 = 0

\Rightarrow x^{2} + x - 2 = 0

\Rightarrow x = - 2 o r 1

Commented by Tawa11 last updated on 28/Jul/22

Great sir

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