A) 7
B) 8
C) 9
D) 10
Correct Answer: C
Solution :
\[x+\frac{1}{x}=1\] or \[{{x}^{2}}-x+1=0\] \[\therefore \,\,x=\frac{1}{2}\pm i\frac{\sqrt{3}}{2}\] or \[x={{e}^{\frac{i\pi }{3}}}\] \[\therefore \,\,\,{{x}^{a}}+{{x}^{-a}}={{e}^{\frac{ia\pi }{3}}}+{{e}^{\frac{-ia}{3}}}=2\cos \frac{a\pi }{3}\] Hence, \[\cos \frac{a\pi }{3}+\cos \frac{b\pi }{3}+\cos \frac{c\pi }{3}=0\] \[a,b,c\in I\,\,\,\,\therefore \,\,a+b+c{{|}_{\min }}=(1+3+5)=9\]You need to login to perform this action.
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