Question:
Short-Answer Questions
Solve: $3 x^{2}+5 \sqrt{5} x-10=0$
Solution:
$3 x^{2}+5 \sqrt{5} x-10=0$
$\Rightarrow 3 x^{2}+6 \sqrt{5} x-\sqrt{5} x-10=0$
$\Rightarrow 3 x(x+2 \sqrt{5})-\sqrt{5}(x+2 \sqrt{5})=0$
$\Rightarrow(x+2 \sqrt{5})(3 x-\sqrt{5})=0$
$\Rightarrow x+2 \sqrt{5}=0$ or $3 x-\sqrt{5}=0$
$\Rightarrow x=-2 \sqrt{5}$ or $x=\frac{\sqrt{5}}{3}$
Hence, $-2 \sqrt{5}$ and $\frac{\sqrt{5}}{3}$ are the roots of the given equation.
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