Question 82
The quadratic equation $a x^{2}+b x+a=0$ ($a, b \neq 0$ and $a \neq b$) is given. Its coefficients are such that the expressions $1, \frac{a+b}{a-b}, \frac{a^{2}+b^{2}}{a^{2}-b^{2}}$ are consecutive terms of an arithmetic sequence. Write down the relation between the coefficients $a$ and $b$, and solve the quadratic equation.