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prove the ratio of the line in the question

Mathematics Asked by sniperking on December 24, 2020

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the book’s solution uses $(a+b)/a= a/b$. I got my answer using b and c but want to understand the book’s method.

One Answer

$$frac{a}{b}=frac{b}{c}$$

$$frac{b}{a}=frac{c}{b}$$

$$frac{b}{a}+1=frac{c}{b}+1$$

$$frac{a+b}{a}=frac{c+b}{b}=frac{a}{b}$$

$$a^2-ba-b^2=0$$

$$a=frac{b(1+sqrt {5})}{2}$$

but

$$a=frac{b(1-sqrt {5})}{2}<0$$

Correct answer by Lion Heart on December 24, 2020

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