Question
The value of $(x^{1/3}+x^{-1/3})(x^{2/3}+x^{-2/3})$ is
Answer: Option A
Answer:(b)$(a+b)(a^2-ab+b^2)=a^3+b^3$$(x^{1/3}+x^{-1/3})(x^{2/3}-1+x^{-2/3})$=$(x^{1/3}+x^{-1/3})((x^{1/3})^2-x^{1/3}.x^{-1/3}+(x^{-1/3})^2)$=$(x^{1/3})^3+(x^{-1/3})^3$$x+x^{-1}=x+1/x$
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Answer:(b)$(a+b)(a^2-ab+b^2)=a^3+b^3$$(x^{1/3}+x^{-1/3})(x^{2/3}-1+x^{-2/3})$=$(x^{1/3}+x^{-1/3})((x^{1/3})^2-x^{1/3}.x^{-1/3}+(x^{-1/3})^2)$=$(x^{1/3})^3+(x^{-1/3})^3$$x+x^{-1}=x+1/x$
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