Question

I need step by step help with: 3x^1/3 + 2x^2/3 =5

Answer 1

If you write
`y=x^(1/3)`, you'll notice this is really just a quadratic equation that can be factorized:


`2x^(2/3)+3x^(1/3)-5=0\iff 2y^2+3y-5=0\iff (2y+5)(y-1)=0\iff(2x^(1/3)+5)(x^(1/3)-1)=0`

So you have


`2x^(1/3)+5=0\implies 2x^(1/3)=-5\implies x^(1/3)=-\frac52\implies x=-\frac{125}8`

and


`x^(1/3)-1=0\implies x^(1/3)=1\implies x=1`