If b is the mean proportional of a and c, then \((a-b)^{3} : (b-c)^{3}\)= ?
Answer & explanation
Correct answer: option 1
b is the mean proportional of a and c
⇒ b² = ac
Now,
\((a-b)^{3} : (b-c)^{3}\)
= \(\frac{ (a - √ac)³ }{(√ac - c )³}\)
= \(\frac{ [√a (√a - √c)]³ }{[√c (√a - √c)]³}\)
= \(\frac{ [√a]³ }{[√c ]³}\)
= \(\frac{ (√a)3/2 }{[√c ]3/2}\)