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# Help needed, please show work

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38
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+44

If a and b are nonzero unequal real numbers and (a−b)/a = b/(a−b), what is the sum of all possible

values for a/b?

Nov 9, 2022

#2
+118135
+3

$$\frac{(a−b)}{a} =\frac{ b}{(a−b)}\\ (a-b)^2=ab\\ a^2-2ab+b^2=ab\\ a^2-3ab+b^2=0\\ a^2+(-3b)a+(b^2)=0\\ a=\frac{3b\pm\sqrt{9b^2-4b^2}}{2}\\ a=\frac{3b\pm b\sqrt{5}}{2}\\$$

$$a=\frac{3b\pm b\sqrt{5}}{2}\\ \frac{a}{b}=\frac{3\pm \sqrt{5}}{2}\\ \text{if you add those two possibilities the sum is } 6/2 = 3$$

You neeed to check this carefully.

Nov 9, 2022