+866 Let u and v be the solutions to 3x^2 + 5x + 7 = -4x^2 + 3x - 14. Find 1/u^2 + 1/v^2.
+1588 We can solve the equation for u and v first:
Combine like terms: 7x^2 + 2x - 21 = 0
Factor the equation: (x - 3)(7x + 7) = 0
Therefore, the solutions are x = 3 and x = -1. These correspond to u = 3 and v = -1.
Now, we need to find 1/u^2 + 1/v^2:
Substitute u = 3 and v = -1: 1/3^2 + 1/(-1)^2
Simplify: (1/9) + (1) = 1/9 + 9/9
Combine terms: 10/9
Therefore, 1/u^2 + 1/v^2 = 10/9.
