+818 Real numbers $x$ and $y$ have an arithmetic mean of $18$ and a geometric mean of $\sqrt{47}$. Find $x^2+y^2$.
+189 Saying that the arithmetic mean of x and y is 18 mathematically means that x+y2=18. Also, saying that x and y have a geometric mean of √47 means that √xy=√47. With this information, we want to find the value of x2+y2. We can use clever algebraic manipulation to find this value without too much trouble.
x+y2=18;√xy=√47x+y=36;xy=47(x+y)2=362x2+2xy+y2=1296x2+y2=1296−2xyx2+y2=1296−2∗47x2+y2=1202
