If $a, b, c$ are in AP and $a^2$, $b^2$, $c^2$ in GP, and $a+b+c=\frac{3}{2}$, then value of $c$ is

Question

$(a)\;\frac{1}{2\sqrt{2}}\qquad(b)\;\frac{1}{2}-\frac{1}{\sqrt{2}}\qquad(c)\;\frac{1}{2}+\frac{1}{\sqrt{2}}\qquad(d)\;\frac{1}{2}$