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Let u and v be the solutions to 3x^2 + 5x + 7 = 2x^2 - 4x - 11.  Find u/v + v/u.

 Sep 20, 2022
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First combine like terms:

x^2 + 9x + 18 = 0 -> (x + 6)(x + 3) = 0.

Either x + 6 or x + 3 = 0 (not both), so x = -6 and x = -3. 

If -6 and -3 are the values of u and v, plugging in we have u/v + v/u, -6/-3 + -3/-6 = 2 + 1/2 = 2.5

 Sep 20, 2022

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