Question

Solve: ${(\frac{7}{4\sqrt{3}+1}+\frac{7}{4\sqrt{3}-1})}^2$

Answer 1

We have,

${(\frac{7}{4\sqrt{3}+1}+\frac{7}{4\sqrt{3}-1})}^2$

$\Rightarrow 49{(\frac{1}{4\sqrt{3}+1}+\frac{1}{4\sqrt{3}-1})}^2$

$\Rightarrow 49{\left(\frac{4\sqrt{3}-1+4\sqrt{3}+1}{(4\sqrt{3}+1)(4\sqrt{3}-1)}\right)}^2$

$\Rightarrow 49{\left(\frac{8\sqrt{3}}{({\left(4\sqrt{3}\right)}^2-1^2)}\right)}^2$

$\Rightarrow 49{\left(\frac{8\sqrt{3}}{(48-1)}\right)}^2$

$\Rightarrow 49{\left(\frac{8\sqrt{3}}{47}\right)}^2$

$\Rightarrow 49\left(\frac{64\times 3}{47\times 47}\right)$

$\Rightarrow \frac{9408}{2209}$

Hence, this is the answer.