71*. Do there exist polynomials $P(x, y)$ and $Q(x, y)$ in two variables $x$ and $y$ such that for all real $x$ and $y$ the equality

$$
(x+y) P(x, y)+(2 x-y-3) Q(x, y)=x^{2}+y^{2} ?
$$
$\triangle$ Let's choose values of $x$ and $y$ such that

$$
x+y=0, \quad 2 x-y-3=0
$$

Solving this system of equations, we will have: $x=1, y=-1$.

Now let's substitute $x=1, y=-1$ into the identity. We get the incorrect equality $0=2$. Therefore, such polynomials do not exist.

Answer: do not exist.