$a)$ $P\left ( X\leq a \right )=\int_{\alpha}^{ a}f(x)dx$
$=\int_{0}^{a }3x^{2}dx$
$=\left [ \frac{-3a^{3}}{3} \right ]=a^{3}$..........................i
$P\left ( X>a \right )$
$=\int_{a}^{\alpha }3x^{2}dx$
$=\int_{a}^{1 }3x^{2}dx$
$=\left [ x^{3} \right ]_{a}^{1}$
$=1-a^{3}$............................................ii
Now, according to question
$a^{3}=1-a^{3}$
$2a^{3}=1$
$a=\frac{1}{\sqrt[3]{2}}$
$b)$ $P(X>b)=0.05$
$\Rightarrow \int_{b}^{\alpha }3x^{2}dx=0.05$
$1-b^{3}=0.05$
$b^{3}=0.95$
$b=\sqrt[3]{0.95}$