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2 problems match “sum and product of roots”. Clear

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1. Sum of squares from means ●○○○○ 10 ptsReal numbers $x$ and $y$ have an arithmetic mean of 18 and a geometric mean of $\sqrt{92}$. Find $x^2+y^2$.
2. Roots of a symmetric odd function ●●●○○ 50 ptsLet $y=f(x)$ be an odd function defined on $\mathbf{R}$ whose graph is symmetric about the line $x=1$. When $0<x\leq 1$, $f(x)=\log_3 x$. Find the sum of all real roots of the equation $f(x)=-\frac{1}{3}+f(0)$ in the interval $(0,10)$.