$T=-\alpha V^3+\beta V^2 \quad \ldots (i)$

and $P V=n R T \quad... (ii)$

$n=1$

So, $P=\frac{R T}{V}$

Multiplying $\frac{R}{V}$ in $(i)$

$\frac{R T}{V}=\left(-\alpha V^2+\beta V\right) R$

or $P=\left(-\alpha V^2+\beta V\right) R \ldots (iii)$

$\frac{d P}{d V}=(-2 \alpha V+\beta) R$

Maxima is when $\frac{d P}{d V}=0$ and $\frac{d^2 P}{d V^2}$ in negative, so

$O=(-2 \alpha V+\beta) R$

$V=\frac{\beta}{2 \alpha}$

Put in value of $V$ in equation $(iii)$

$P=\left(-\alpha \frac{\beta^2}{4 \alpha^2}+\frac{\beta^2}{2 \alpha}\right) R \Rightarrow P=\frac{\beta^2 R}{4 \alpha}$