Real numbers $x$ and $y$ have an arithmetic mean of 7 and a geometric mean of $\sqrt{19}$. Find $x^2+y^2$.

Guest Feb 26, 2020

#1**+1 **

(x+y)/2 = 7 square both sides and re-arrange: x^2 + 2xy + y^2 =196

sqrt (xy) = sqrt19

xy = 19

x^2 + 2(19) +y^2 = 196

x^2 + y^2 = 158

ElectricPavlov Feb 26, 2020