Question 33
a. Prove that for all real numbers $x$ and $y$,
$$
x^{2}-2 y^{2}=-\left[(x+2 y)^{2}-2(x+y)^{2}\right] .
$$
b. How many positive integer solutions does the equation $x^{2}-2 y^{2}=1$ have?
c. How many positive integer solutions does the equation $x^{2}-2 y^{2}=5$ have?
$$
x^{2}-2 y^{2}=-\left[(x+2 y)^{2}-2(x+y)^{2}\right] .
$$
b. How many positive integer solutions does the equation $x^{2}-2 y^{2}=1$ have?
c. How many positive integer solutions does the equation $x^{2}-2 y^{2}=5$ have?