Algebra and Applications Test 3

ax + by = 3
bx - ay = 4
and ${\mathit{x}}^2+{\mathit{y}}^2=1$
From the above equation, it is clear that the values of x and y are $\frac{1}{\sqrt{2}},\frac{1}{\sqrt{2}}$ respectively
Now, $\frac{\mathit{a}}{\sqrt{2}}+\frac{\mathit{b}}{\sqrt{2}}=3$
$\frac{\mathit{b}}{\sqrt{2}}-\frac{\mathit{a}}{\sqrt{2}}=4$
$\mathit{a}+\mathit{b}=3\sqrt{2}$......(i)
$\mathit{b}-\mathit{a}=4\sqrt{2}$......(ii)
Squaring both the sides of equation (i) and (ii) and adding we get:
$2\left({\mathit{a}}^2+{\mathit{b}}^2\right)=50$
Value of ${\mathit{a}}^2+{\mathit{b}}^2=25$