if-x-2-1-3-2-1-3-2-x-2-1-3-1-3-2-then-find-the-value-of-198x-4-868x-3-229x-2-200x-

Question Number 152772 by Rankut last updated on 01/Sep/21

i f \sqrt[3]{\sqrt[3]{x - 2} + 2} + \sqrt[3]{2 - \sqrt[3]{x - 2}} = 2

then find the value of

\sqrt{198 x^{4} - 868 x^{3} - 229 x^{2} + 200 x}

Commented by Rankut last updated on 01/Sep/21

a n y h e l p p l e a s e

Commented by MJS_new last updated on 01/Sep/21

typo ?

{there}^{'} s a similae question \dots just scroll down

to find it

Answered by mr W last updated on 01/Sep/21

l e t t = \sqrt[3]{x - 2}

\sqrt[3]{2 + t} + \sqrt[3]{2 - t} = 2

2 + t + 2 - t + 3 \times 2 \sqrt[3]{4 - t^{2}} = 8

3 \sqrt[3]{4 - t^{2}} = 2

27 (4 - t^{2}) = 8

t = \pm \sqrt{4 - \frac{8}{27}} = \pm \frac{10 \sqrt{3}}{9}

x = 2 + t^{3} = 2 \pm \frac{1000 \sqrt{3}}{243}

\dots \dots

Commented by Rankut last updated on 01/Sep/21

t h a n k y o u s i r

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