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

Question

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

Answer 1

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