Question-187989

Question Number 187989 by mnjuly1970 last updated on 24/Feb/23

Answered by HeferH last updated on 24/Feb/23

b^{2} = a c

b^{3} = a b c

\frac{b^{3} c^{3} + a^{3} c^{3} + a^{3} b^{3}}{a^{3} b^{3} c^{3}} \cdot (\frac{a^{2} b^{2} c^{2}}{a^{3} + b^{3} + c^{3}}) =

\frac{b^{3} c^{3} + a^{3} c^{3} + a^{3} b^{3}}{a b c} \cdot (\frac{1}{a^{3} + b^{3} + c^{3}}) =

\frac{{(b c)}^{3} + b^{6} + {(a b)}^{3}}{b^{3}} \cdot (\frac{1}{a^{3} + b^{3} + c^{3}}) =

c^{3} + b^{3} + a^{3} \cdot (\frac{1}{a^{3} + b^{3} + c^{3}}) = 1

Answered by MathGuy last updated on 24/Feb/23

A n s w e r : -

\frac{a^{2} b^{2} c^{2}}{a^{3} + b^{3} + c^{3}} (\frac{b^{3} c^{3} + c^{3} a^{3} + a^{3} b^{3}}{a^{3} b^{3} c^{3}})

\Rightarrow \frac{1}{a^{3} + b^{3} + c^{3}} (\frac{b^{3} c^{3} + c^{3} a^{3} + a^{3} b^{3}}{a b c})

\Rightarrow \frac{1}{a^{3} + b^{3} + c^{3}} (\frac{b^{2} c^{2}}{a} + \frac{c^{2} a^{2}}{b} + \frac{a^{2} b^{2}}{c})

s u b s t i t u t e b^{2} = a c & c^{2} a^{2} = b^{2}, i n t h e e x p r e s s i o n

u n d e r b r a c k e t s a n d s i m p l i f y .

y o u w i l l g e t

\frac{1}{a^{3} + b^{3} + c^{3}} (a^{3} + b^{3} + c^{3})

= 1

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