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harina [27]
3 years ago
10

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

Mathematics
1 answer:
Luba_88 [7]3 years ago
5 0
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
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