Question

$3x { }^{2} - 36 = 0$
$\sqrt{3} x { }^{2} - \sqrt{81 } = 0$

$9x { }^{2} + 81 = 0$
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Answer 1

3x² - 36 = 0

3x² = 36

x² = 36 : 3 = 12

x₁,₂ = ±√12 = ±2√3

√3 · x² - √81 = 0

√3 · x² = √81

x² = √81 : √3 = √27 = 3√3

x₁ = $\sqrt{3\sqrt{3}}=\sqrt{3*3^{\frac{1}{2}}}=\sqrt{3^{\frac{3}{2}}}=3^{\frac{3}{4}}$, x₂ = $-\sqrt{3\sqrt{3}}=-\sqrt{3*3^{\frac{1}{2}}}=-\sqrt{3^{\frac{3}{2}}}=-3^{\frac{3}{4}}$

9x² + 81 = 0

9x² = -81

x² = -81 : 9 = -9

x₁ = $\sqrt{-9}=\sqrt{-1}*\sqrt{9}=3i$, x₂ = $-\sqrt{-9}=-\sqrt{-1}*\sqrt{9}=-3i$

/robertinni