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Factorize:$2x^2 + 3\sqrt{5}x + 5$
Given :
$2x^2 + 3\sqrt{5}x + 5$
To do :
We have to factorize the given expression.
Solution :
$2 x^{2}+3 \sqrt{5} x+5 = 2 x^{2}+2 \sqrt{5} x+\sqrt{5} x+5$ {Since $3 \sqrt{5}=2 \sqrt{5} +\sqrt{5}$ and $2 \sqrt{5} \times \sqrt{5}=10=2\times5$]
$=2 x(x+\sqrt{5})+\sqrt{5}(x+\sqrt{5})$
$=(x+\sqrt{5})(2 x+\sqrt{5})$
Hence, $2 x^{2}+3 \sqrt{5} x+5 =(x+\sqrt{5})(2 x+\sqrt{5})$.
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