$N=\sum f_i=40+\alpha+\beta$

$\sum f_i x_i=360+6 \alpha+12 \beta$

$\sum f _{ i } x _{ i }^2=3904+36 \alpha+144 \beta$

$\operatorname{Mean}(\overline{ x })=\frac{\sum f _{ i } x _{ i }}{\sum f _{ i }}=9$

$\Rightarrow 360+6 \alpha+12 \beta=9(40+\alpha+\beta)$

$3 \alpha=3 \beta \Rightarrow \alpha=\beta$

$\sigma^2=\frac{\sum f _{ i } x _1^2}{\sum f _{ i }}-\left(\frac{\sum f _{ i } x _{ i }}{\sum f _{ i }}\right)^2$

$\Rightarrow \frac{3904+36 \alpha+144 \beta}{40+\alpha+\beta}-(\overline{ x })^2=15.08$

$\Rightarrow \frac{3904+180 \alpha}{40+2 \alpha}-(9)^2=15.08$

$\Rightarrow \alpha=5$

Now, $\alpha^2+\beta^2-\alpha \beta=\alpha^2=25$