+1167 Let a and b be the solutions to 7x^2 + x - 5 = 6x^2 - 5x + 12. Compute 1/(a^2 - 4) + 1/(b^2 - 4).
+129771 Rearrange as
x^2 + 6x - 17 = 0
ab = -17
2ab = -34
a + b = -6 square both sides
a^2 + 2ab + b^2 = 36
a^2 + b^2 - 34 = 36
a^2 + b^2 = 70
1/(a^2 - 4) + 1/(b^2 - 4) =
[ a^2 + b^2 - 8 ] / [ (ab)^2 - 4(a^2 + b^2) + 16 ] =
[ 70 - 8 ] / [ (-17)^2 - 4(70) +16 ] =
[62] / [ 25]
