Question

$\frac{3x {}^{2} }{2} = (3 - 2 \sqrt{3 } ) {}^{2}$


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Answer 1

$\frac { 3 x ^ { 2 } } { 2 } = ( 3 - 2 \sqrt { 3 } ) ^ { 2 }$

$3x^{2}=2\left(3-2\sqrt{3}\right)^{2}$

$3x^{2}=2\left(9-12\sqrt{3}+4\left(\sqrt{3}\right)^{2}\right)$

$3x^{2}=2\left(9-12\sqrt{3}+4\times 3\right)$

$3x^{2}=2\left(9-12\sqrt{3}+12\right)$

$3x^{2}=2\left(21-12\sqrt{3}\right)$

$3x^{2}=42-24\sqrt{3}$

$\frac{3x^{2}}{3}=\frac{42-24\sqrt{3}}{3}$

$x^{2}=\frac{42-24\sqrt{3}}{3}$

$x^{2}=14-8\sqrt{3}$

$x=\sqrt{2}\left(2-\sqrt{3}\right)$

$x=-\sqrt{2}\left(2-\sqrt{3}\right)$

Sper ca ti-am fost de folos. Succes!!