Answer
The solution of the equation is\[-\frac{54+43\sqrt{2}}{46}\].
Work Step by Step
Consider the equation:
$\frac{7+4\sqrt{2}}{2-5\sqrt{2}}$.
Then rationalize the denominator as,
$\begin{align}
& \frac{7+4\sqrt{2}}{2-5\sqrt{2}}=\frac{\left( 7+4\sqrt{2} \right)}{\left( 2-5\sqrt{2} \right)}\times \frac{\left( 2+5\sqrt{2} \right)}{\left( 2+5\sqrt{2} \right)} \\
& =\frac{14+35\sqrt{2}+8\sqrt{2}+40}{4-50} \\
& =\frac{54+43\sqrt{2}}{-46} \\
& =-\frac{54+43\sqrt{2}}{46}
\end{align}$
Hence, the solution of the equation is $-\frac{54+43\sqrt{2}}{46}$.
