if-a-2b-2-b-2c-2-0-find-volve-b-c-a-3-abc-

Question Number 163651 by mathlove last updated on 09/Jan/22

i f {(a - 2 b)}^{2} + {(b - 2 c)}^{2} = 0

f i n d v o l v e \frac{{(b + c - a)}^{3}}{a b c} = ?

Commented by cortano1 last updated on 09/Jan/22

\begin{matrix} a = 2 b \Rightarrow b = \frac{1}{2} a \\ b = 2 c \Rightarrow c = \frac{1}{4} a \end{matrix}} \Rightarrow \frac{- \frac{1}{64} a^{3}}{\frac{1}{8} a^{3}} = - \frac{1}{8}

Answered by Rasheed.Sindhi last updated on 09/Jan/22

a = 2 b \land b = 2 c \Rightarrow a = 2 (2 c) = 4 c

\frac{{(b + c - a)}^{3}}{a b c} = \frac{{(2 c + c - 4 c)}^{3}}{4 c . 2 c . c} = \frac{- c^{3}}{8 c^{3}} = - \frac{1}{8}