+660 1. Let a and b be the solutions to \(5x^2-11x+4=2x^2+7x-9\). Find \(1/a+ 1/b\).
2. Let u and v be the solutions to \(3x^2+5x+7=-x^2+4x-4\). Find \(u/v+v/u\).
+129885 First one
3x^2 - 18x + 13 = 0
ab = 13/3
a + b = 18/3 = 6
1/a + 1/b = (a + b) / (ab) = 6 / (13/3) = 18 / 13
Second one
4x^2 + x + 11 = 0
uv = 11/4
u + v = - 1/4 square both sides
u^2 + 2(uv) + v^2 = 1/16
u^2 + 2(11/4) + v^2 = 1/16
u^2 + v^2 = 1/16 - 22/4
u^2 + v^2 = -87 / 16
u / v + v /u =
[ u^2 + v^2 ] / [ uv ] = (-87/16) /( 11/4) = (-87/16)(4/11) = -87/44
