Solve: 2x^(2/3) - 5x^(1/3)-3 = 0.

Question

Accepted Answer

Welcome back. I'm so glad you're here. We get to solve for X. Our equation is x minus two equals the square root of two. X minus five. Alright. We want to get X by itself but on that right hand side the X is trapped inside that radical. Poor thing. So let's free it from the bonds of that radical and we will square it. But what we do to one side we do need to do to the other side too. So the right hand side of this equation that's looking good. The square root of two, X minus five squared is just two x minus five. But the left hand side when you have parentheses X minus two squared, that is going to be parentheses X minus two times parentheses X minus two. And we do in fact need to foil that out. So let's do that. Are firsts X times X. Is X squared. Our Outsides X times negative two. That's minus two X. Our insides negative two times X also minus two X. And our last negative two times negative two is plus four equals bring down the right hand side two X minus five. Let's combine our like terms minus two x minus two X. Is going to be minus four X. Bring down the rest. So it's X squared minus four X plus four equals two X minus five. All right. We've got a quadratic here. So let's bring everything on the right hand side. This two X and this minus five over to the left hand side so that the right will be equal to zero. So subtracting two X from both sides and adding five to both sides will give us X squared still and negative four X minus two. X is minus six X plus four plus five. That's plus nine equals zero. And yeah we can factor this. What times what gives us X squared. That's X times X. What? Two numbers when multiplied? Give us a positive nine but add up to a negative six, that's minus three minus three. And normally I'd say okay we've got two factors. Let's set them both equal to zero but they're the same thing. So we'll just set x minus three equal to zero and we'll add three to both sides to solve for X where X equals three. Yay, Alright. We look at our original equation and we ask ourselves does it make sense that there is one solution for X and Yeah X had a degree of one in our original solution. So we look at our answer choices and that matches with answer choice. A well done. We'll catch you on the next one

Solve: 2x^(2/3) - 5x^(1/3)-3 = 0.

Key Concepts

Rational Exponents

Substitution Method

Quadratic Equations

Watch next