MCQ
$\sum {{1 \over {1 + {x^{a - b}} + {x^{a - c}}}} = } $
- ✓$1$
- B$-1$
- C$0$
- DNone of these
= ${1 \over {{x^{b + c}} + {x^{c + a}} + {x^{a + b}}}}\sum\limits_{}^{} {{x^{b + c}}} $
= ${1 \over {{x^{b + c}} + {x^{c + a}} + {x^{a + b}}}}\,({x^{b + c}} + {x^{c + a}} + {x^{a + b}}) = 1$.
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$x^{2}-\left(5+3 \sqrt{\log _{3} 5}-5 \sqrt{\log _{5} 3}\right)x+3\left(3^{\left(\log _{3} 5\right)^{\frac{1}{3}}}-5^{\left(\log _{5} 3\right)^{\frac{2}{3}}}-1\right)=0$
then the equation, whose roots are $\alpha+\frac{1}{\beta} \text { and } \beta+\frac{1}{\alpha} \text {, }$