+207 Let u and v be the solutions to 3x^2 + 5x + 7 = 2x^2 + 11x - 6. Find u/v^2 + v/u^2.
+129847 Simplify as
x^2 - 6x + 13
uv = 13
2uv = 26
u + v = 6 square both sides
u^2 + 2uv + v^2 = 36
u^2 + 26 + v^2 = 36
u^2 + v^2 = 10
u/v^2 + v/u^2 = [ u^3 + v^3 ] / [ uv]^2
u^3 + v^3 = ( u + v) ( u^2 + v^2 - uv) = (6)(10 - 13) = -18
[uv]^2 = [ 13]^2 = 169
u/v^2 + v/u^2 = [ u^3 + v^3 ] / [ uv]^2 = -18 / 169
