# Answer to Question #21921 in Abstract Algebra for M E Haider

Question #21921

If x+1/x is not equal to 0 for any real value

and x to the power 3 + 1/x to the power 3=0

find x to the power 5 + 1/x to the power 5

and x to the power 3 + 1/x to the power 3=0

find x to the power 5 + 1/x to the power 5

Expert's answer

x^3+1/x^3=0

hence (x^6+1)/x^3=0

x^6+1=0

x^6=-1x^6>=0 for all real numbers, thus, x^6 can't be equal to-1 therefore x can't be real number

hence (x^6+1)/x^3=0

x^6+1=0

x^6=-1x^6>=0 for all real numbers, thus, x^6 can't be equal to-1 therefore x can't be real number

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