A) 1
B) \[-\,\,1\]
C) 0
D) None of these
Correct Answer: A
Solution :
As given, \[{{\left( \frac{{{x}^{a}}}{{{x}^{b}}} \right)}^{{{a}^{2}}+ab+{{b}^{2}}}}\times {{\left( \frac{{{x}^{b}}}{{{x}^{c}}} \right)}^{{{b}^{2}}+bc+{{c}^{2}}}}\times {{\left( \frac{{{x}^{c}}}{{{x}^{a}}} \right)}^{{{c}^{2}}+ac+{{a}^{2}}}}\] \[={{x}^{(a-b)({{a}^{2}}+ab+{{b}^{2}})}}\times {{x}^{(b-c)({{b}^{2}}+bc+{{c}^{2}})}}\times {{x}^{(c-a)({{c}^{2}}+ac+{{a}^{2}})}}\] \[={{x}^{{{a}^{3}}-{{b}^{3}}}}\cdot {{x}^{{{b}^{3}}-{{c}^{3}}}}\cdot {{x}^{{{c}^{3}}-{{a}^{3}}}}\] \[[\because ({{a}^{3}}-{{b}^{3}})=(a-b)({{a}^{2}}+ab+{{b}^{2}})]\] \[={{x}^{{{a}^{3}}-{{b}^{3}}+{{b}^{3}}-{{c}^{3}}+{{c}^{3}}-{{a}^{3}}}}={{x}^{0}}=1\]
You need to login to perform this action.
You will be redirected in
3 sec
