Ratios issue

[parthp24]

Been working at this ratios problem for a while and cant seem to get it: Suppose a,b,c > 0 and (a/b)=(b/c) Prove that (a+b)/(b+c) = sqrt(a/c)

I've managed to successfully prove (a+b)/(b+c)=a/b=/bc but im stuck on the sqrt(a/c) part.

 

[Dr.Peterson]

Been working at this ratios problem for a while and cant seem to get it: Suppose a,b,c > 0 and (a/b)=(b/c) Prove that (a+b)/(b+c) = sqrt(a/c)

I've managed to successfully prove (a+b)/(b+c)=a/b=/bc but im stuck on the sqrt(a/c) part.

I don't know what techniques you have learned; but I like to give a name to the ratio, e.g. a/b = b/c = k, and then express a and b in terms of k and c. Then put that into (a+b)/(b+c) and sqrt(b/c), and show that they both equal k.

 

[lex]

I've managed to successfully prove (a+b)/(b+c)=a/b=b/c but im stuck on the sqrt(a/c) part.

Then you're done, because [MATH]\frac{b}{c}[/MATH] can be transformed into the answer you want.
Simply rewrite the first equation, making [MATH]b[/MATH] the subject of [MATH]\frac{a}{b}=\frac{b}{c}[/MATH] and substitute that into your [MATH]\frac{b}{c}\ [/MATH]