Question

If $\frac{(x-2\sqrt{6})(5\sqrt{3}+5\sqrt{2})}{5\sqrt{3}-5\sqrt{2}}=1$ then the value of x is

• A. 7
• B. 4
• C. 6
• D. 5

Answer 1

The correct option is D 5

$\frac{(x-2\sqrt{6})(5\sqrt{3}+5\sqrt{2})}{5\sqrt{3}-5\sqrt{2}}=1$
$\Rightarrow x-2\sqrt{6}=\frac{5\sqrt{3}-5\sqrt{2}}{5\sqrt{3}+5\sqrt{2}}=\frac{5\sqrt{3}-5\sqrt{2}}{5\sqrt{3}+5\sqrt{2}}\times \frac{5\sqrt{3}-5\sqrt{2}}{5\sqrt{3}-5\sqrt{2}}=\frac{{(5\sqrt{3}-5\sqrt{2})}^2}{{\left(5\sqrt{3}\right)}^2-{\left(5\sqrt{2}\right)}^2}$

$\Rightarrow x-2\sqrt{6}=\frac{{\left(5\sqrt{3}\right)}^2+{\left(5\sqrt{2}\right)}^2-2\times 5\sqrt{3}\times 5\sqrt{2}}{75-50}=\frac{(75+50-50\sqrt{6})}{25}=5-2\sqrt{6}$
$\Rightarrow x-2\sqrt{6}=5-2\sqrt{6}$
$\Rightarrow x=5$
Hence, the correct option is d.