Question

a :b = b : c, then proof that a²b²c²(1/a³ + 1/b³ + 1/c³)= a³+b³+c³​

Answer 1

acc to me there is some prblm in this Question

if u got this answer then plz tell me too

Answer 2

Solution

a:b = b:c

$a\: =\: \dfrac{b^2}{c}$

Let take LHS of Equation

$a^2b^2c^2\Big(\dfrac{1}{a^3}\: +\: \dfrac{1}{b^3}\: +\: \dfrac{1}{c^3}\Big)$

Let we put value of a in equation after simplification

$\dfrac{a^2b^2c^2}{a^3}\: +\: \dfrac{a^2b^2c^2}{b^3}\: +\: \dfrac{a^2b^2c^2}{c^3}$

$\dfrac{b^2c^2}{a}\: +\: \dfrac{a^2c^2}{b}\: +\: \dfrac{a^2b^2}{c}$

$\dfrac{b^2c^2}{\dfrac{b^2}{c}}\: +\: \dfrac{\Big(\dfrac{b^2}{c}\Big)^2c^2}{b}\: +\: a^2.a$

$\dfrac{b^2c^2.c}{b^2}\: +\: \dfrac{\dfrac{b^4}{c^2}c^2}{b}\: +\: a^2.a$

$c^2.c \:+\: \dfrac{b^4}{c^2}\times\dfrac{c^2}{b}+\: a^2.a$

$c^3 \:+\: b^3+\: a^3$

Rearrange the sequence

$\boxed{a^3 \:+\: b^3+\: c^3}$

RHS

LHS = RHS

Hence Proved