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a and b are the roots of 2x^2 - 3x - 1 = 0.  Find a/b + b/a.

Jun 24, 2020

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There's not a simple way to factorize $$2x^2 - 3x - 1 = 0$$, so instead we simplify $$\frac{a}{b}+\frac{b}{a}=\frac{a^2+b^2}{ab}=\frac{(a+b)^2-2ab}{ab}=\frac{(a+b)^2}{ab}-2$$

Using Vieta's Formula, a+b = 3/2 and ab = -1/2.

Plug these in to get $$\frac{(3/2)^2}{-1/2}-2=\frac{9/4}{-1/2}-2=-\frac{9}{2}-2=\frac{-13}{2}$$

Jun 24, 2020