Browse · MATH Print → jmc algebra intermediate Problem Real numbers x and y have an arithmetic mean of 7 and a geometric mean of 19. Find x2+y2. Solution — click to reveal The givens tell us that 2x+y=7 and xy=19, or x+y=14 and xy=19. (x+y)2=x2+2xy+y2, so x2+y2=(x+y)2−2xy=142−2⋅19=196−38=158 Final answer 158 ← Previous problem Next problem →