Question

If a,b,c are in continued proportion prove that
(a+b) : (b+c) :: a²(b–c) : b²(a–b)

Answer 1

Answer:

Step-by-step explanation:

If a,b,c are in continued proportion, then $\frac{a}{b}=\frac{b}{c}$  or $\frac{a+b}{b}=\frac{b+c}{c}$ or b^2=ac

Also, $\frac{a-b}{b} =\frac{b-c}{c}$ implies $\frac{b-c}{a-b} =\frac{c}{b}$.

Now, ( $\frac{a^{2} }{b^{2} }$)($\frac{b-c}{a-b}$) = $\frac{a^{2} }{b^{2} } . \frac{c}{b} = \frac{b^{2} }{c^{2} }.\frac{b}{c} = \frac{b}{c}= \frac{a+b}{b+c}$.

as \frac{a}{b}=\frac{b}{c}.

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