A) -1
B) 4
C) 3
D) - 4
Correct Answer: C
Solution :
\[{{\left[ \frac{({{x}^{1/3}}+1)\,({{x}^{2/3}}-{{x}^{1/3}}+1)}{({{x}^{2/3}}-{{x}^{1/3}}+1)}-\frac{(\sqrt{x}-1)(\sqrt{x}+1)}{\sqrt{x}(\sqrt{x}-1)} \right]}^{10}}\] \[={{({{x}^{1/3}}\,+1-1-1/{{x}^{1/2}})}^{10}}\] \[=({{x}^{1/3}}\,-1/{{x}^{1/2}})\] \[r=1/3,\,b=1/2\] \[r=\frac{\frac{10}{3}-(-5)}{1/3+\frac{1}{2}}\] \[r=\frac{25/3}{\left( 5\frac{1}{2} \right)}\,=10\] \[\cos .\,=10{{c}_{10}}\,(1)\,{{(-1)}^{10}}\,=1\]
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