Take quadratic equation x^2-6x+14=0 and its solutions a and b. What is a/b+b/a?
In this kind of exersise it is easy to use Viète's formula for quadratic equations: Let: a+b = S ab=P then x2 -Sx + P=0 In our case, S=6 and P=14 by multiplying the fractions we get: (aa)/(ab)+(bb)/(ab) = 2(a+b)/ab= 2S/P = 12/14 = 6/7
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