Question

solve it please.....................

Answer 1

Hello Mate!

Take you solution :-

$\frac{1}{1 + {x}^{b - a} + {x}^{c - a} } + \frac{1}{1 + {x}^{a - b} + {x}^{c - b } } + \frac{1}{1 + {x}^{a - c} + {x}^{b - c} } = 1$

Now multiply terms with x^a, x^b , x^c respectively.

$\frac{ {x}^{a} }{ {x}^{a} + {x}^{b} + {x}^{c} } + \frac{ {x}^{b} }{ {x}^{b} + {x}^{a} + {x}^{c} } + \frac{ {x}^{c} }{ {x}^{c} + {x}^{a} + {x}^{b} } = 1$

Now, all denominators are equal so,

$\frac{ {x}^{a} + {x}^{b} + {x}^{c} }{ {x}^{a} + {x}^{b} + {x}^{c } } = 1 \\ 1 = 1$

Hope it helps☺!