Question-149043

Question Number 149043 by Tawa11 last updated on 02/Aug/21

Commented by EDWIN88 last updated on 02/Aug/21

x = 2

Commented by Tawa11 last updated on 02/Aug/21

Workings sir .

Commented by Tawa11 last updated on 02/Aug/21

Solve for x

Answered by EDWIN88 last updated on 02/Aug/21

2 \sqrt{x} (u - v) = 4 \sqrt{3}

w h e r e {\begin{cases} u = \sqrt{x} + \sqrt{x + \sqrt{3}} \\ v = \sqrt{x} - \sqrt{x - \sqrt{3}} \end{cases}

\Leftrightarrow 2 \sqrt{x} (\sqrt{x + \sqrt{3}} + \sqrt{x - \sqrt{3}}) = 4 \sqrt{3}

\Leftrightarrow \sqrt{x^{2} + x \sqrt{3}} + \sqrt{x^{2} - x \sqrt{3}} = 2 \sqrt{3}

\Rightarrow 2 x^{2} + 2 \sqrt{x^{4} - 3 x^{2}} = 12

\Rightarrow \sqrt{x^{4} - 3 x^{2}} = 6 - x^{2}

\sqrt{u^{2} - 3 u} = 6 - u; u = x^{2}

u^{2} - 3 u = 36 - 12 u + u^{2}

\Rightarrow 9 u = 36 \Rightarrow u = 4

t h e n x = 2, s i n c e x = - 2 r e j e c t e d

Commented by bramlexs22 last updated on 02/Aug/21

nice

Commented by Tawa11 last updated on 02/Aug/21

Thank you sir . God bless you

Commented by Tawa11 last updated on 22/Aug/21

Sir . I could not get the first part since .

That is : 2 \sqrt{x} (u - v) = 4 \sqrt{3}

But I understand other steps very well .

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