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Question Number 166695 by amin96 last updated on 25/Feb/22

Answered by som(math1967) last updated on 25/Feb/22

$$(x^{x+\frac{1}{x}}+1+1+x^{x+\frac{1}{x}})$$$$=x^3+\frac{1}{x^3}+2[x+\frac{1}{x}=3]$$$$={(x+\frac{1}{x})}^3-3(x+\frac{1}{x})+2$$$$=3^3-9+2=20$$

Answered by MJS_new last updated on 25/Feb/22

$$(x^x+{\left(1/x\right)}^{1/x})(x^{1/x}+{\left(1/x\right)}^x)=$$$$=x^{x+\frac{1}{x}}+\frac{1}{x^{x+\frac{1}{x}}}+2=x^3+\frac{1}{x^3}+2=$$$$={(x+\frac{1}{x}-1)}^2(x+\frac{1}{x}+2)=2^2\times 5=20$$

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