solve-for-x-x-x-11-x-10-find-x-x-

Question Number 171821 by Mikenice last updated on 21/Jun/22

s o l v e f o r x :

x \sqrt{x} - 11 \sqrt{x} = 10, f i n d x - \sqrt{x}

Commented by mr W last updated on 21/Jun/22

l e t t = \sqrt{x} > 0

t^{3} - 11 t - 10 = 0

t^{3} + t^{2} - t^{2} - t - 10 t - 10 = 0

(t + 1) (t^{2} - t - 10) = 0

\Rightarrow t = - 1 < 0 r e j e c t e d

\Rightarrow t^{2} - t - 10 = 0

\Rightarrow t^{2} - t = 10, i . e . x - \sqrt{x} = 10 ✓

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