What are the values of x in the equation #x^(2/5) + x^(1/5) + 1 = 3#?

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Answer 1 · 2018-05-09T23:13:58

The two solutions are #x=1# and #-32#.

Make a substitution to make the equation easier to solve:

#x^(2/5)+x^(1/5)+1=3#

#x^(2/5)+x^(1/5)-2=0#

#(x^(1/5))^2+x^(1/5)-2=0#

Let #u=x^(1/5)#:

#u^2+u-2=0#

#(u+2)(u-1)=0#

#u=-2,1#

Put #x^(1/5)# back in for #u#:

#color(white){color(black)( (x^(1/5)=-2,qquadquadx^(1/5)=1), (x=(-2)^5,qquadquadx=(1)^5), (x=-32,qquadquadx=1):}#

Those are the two solutions. Hope this helped!