If x − y = 7 and xy = 9,

$x-y=7$

$\Rightarrow$ On squaring both the sides :

$\Rightarrow(x-y)^{2}=(7)^{2}$

$\Rightarrow x^{2}+y^{2}-2 x y=49$

$\Rightarrow x^{2}+y^{2}=49+2 x y$

Given:

$x y=9$

$\Rightarrow x^{2}+y^{2}=49+2(9)$

$\Rightarrow x^{2}+y^{2}=49+18$

$\Rightarrow x^{2}+y^{2}=67$

Therefore, the value of $x^{2}+y^{2}$ is 67 .