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