Question

please help me with this problem​

Answer 1

Answer:

Hey mate here is your answer ✨

-1...

Answer 2

Answer :-

Value is (B) 1

Explanation :-

$\huge \mathsf{ \dfrac{1}{1 + x^{b - a} + x^{c - a} } + \dfrac{1}{1 + x^{a - b} + x^{c - b} } + \dfrac{1}{1 + x^{b - c} + x^{a - c} } }$

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

$\boxed{ \bf \because p^{m - n} = \dfrac{ p^m }{p^n} }}$

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

$\huge \mathsf{ = \dfrac{x^a}{x^a + x^b + x^c }+ \dfrac{x^b} {x^b + x^a + x^c} + \dfrac{x^c }{x^c + x^b + x^a } }$

Taking LCM

$\huge \mathsf{ = \dfrac{x^a + x^b + x^c }{x^a + x^b + x^c }}$

$\huge \mathsf{ = 1}$

∴ the value is (B) 1