$$\left. \begin{array} { l } { x = 3 + \sqrt { 8 } } \\ { x ^ { 2 } + \frac { 1 } { x ^ { 2 } } } \end{array} \right.$$
Solve for x, y
$y=34$
Solution Steps
Consider the first equation. Factor $8=2^{2}\times 2$. Rewrite the square root of the product $\sqrt{2^{2}\times 2}$ as the product of square roots $\sqrt{2^{2}}\sqrt{2}$. Take the square root of $2^{2}$.
$$x=3+2\sqrt{2}$$
Consider the second equation. Insert the known values of variables into the equation.
Consider $\left(17+12\sqrt{2}\right)\left(17-12\sqrt{2}\right)$. Multiplication can be transformed into difference of squares using the rule: $\left(a-b\right)\left(a+b\right)=a^{2}-b^{2}$.
