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

$2x^{1/3}+5=0\implies 2x^{1/3}=-5\implies x^{1/3}=-\dfrac52\implies x=-\dfrac{125}8$

and

$x^{1/3}-1=0\implies x^{1/3}=1\implies x=1$