Question

x²/3 + 1/2 = 2

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Answer 1

$\frac{x^2}{3}+\frac{1}{2}=2\quad :\quad x=\frac{3\sqrt{2}}{2},\:x=-\frac{3\sqrt{2}}{2}\quad \left(\mathrm{Decimal}:\quad x=2.12132\dots ,\:x=-2.12132\dots \right)$

$\frac{x^2}{3}+\frac{1}{2}=2$

$\frac{x^2}{3}+\frac{1}{2}-\frac{1}{2}=2-\frac{1}{2}$

$\frac{x^2}{3}=2-\frac{1}{2}$

$\frac{x^2}{3}=\frac{2\cdot \:2}{2}-\frac{1}{2}$

$\frac{x^2}{3}=\frac{2\cdot \:2-1}{2}$

$\frac{x^2}{3}=\frac{3}{2}$

$\frac{3x^2}{3}=\frac{3\cdot \:3}{2}$

$x^2=\frac{9}{2}$

$x=\sqrt{\frac{9}{2}},\:x=-\sqrt{\frac{9}{2}}$

$x=\frac{3\sqrt{2}}{2},\:x=-\frac{3\sqrt{2}}{2}$