1. The graphs of the functions $y=x^{2}+a x+b$ and $y=x^{2}+c x+d$ intersect at the point with coordinates $(1,1)$. Compare $a^{5}+d^{6}$ and $c^{6}-b^{5}$.
# Solution

Since the graphs pass through the point $(1,1)$, then $1=1+a+b$ and $1=1+c+d$, which means $a=-b$ and $c=-d$. Therefore, $a^{5}=-b^{5}$ and $d^{6}=c^{6}$. Adding these equations, we get $a^{5}+d^{6}=c^{6}-b^{5}$.

## Answer these numbers are equal