+660 1. Let a and b be the solutions to 5x2−11x+4=2x2+7x−9. Find 1/a+1/b.
2. Let u and v be the solutions to 3x2+5x+7=−x2+4x−4. Find u/v+v/u.
+130458 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
