Solve each equation in Exercises 96–102 by the method of your cho...

Question

Solve each equation in Exercises 96–102 by the method of your choice. 2√(x-1) = x

Accepted Answer

Welcome back. I'm so glad you're here. We are solving for X. And we've got an X on both sides of the equation and one of those exes is trapped under the square root bracket and we've got to free it. So let's start by freeing that X on the left side. How do we free it from the square root bracket? We will square it. And what we do to one side? We've got to do to the other. So now we're looking at two X minus one equals X squared. Great. No more square roots. Now, how do we get those exes together? Well, let's bring them all over to the right side so that we're just dealing with the positive X squared. So we're going to have X squared minus two X plus one equal to zero. And that looks like it could be factored. So we'll give it a try. So what times what gives us this first term? R X squared? Well that could be X times X. And what times what gives us this last term? Well that could be one times one. Or it could be negative one times negative one. And which of those is going to add up to be negative two X. Well that's going to be the second one, negative one times negative one. So we'll have X minus one times X minus one. And look at that. Those are the same thing. And it's also as factored as it's going to get. So we can say zero equals X minus one. To solve for X will add wonderful sides. And that gives us X equals one and great. We have an answer. But before we declare victory, we need to go back and look and see if there were any domain restrictions and having a square root involved could cause domain issues. So let's plug it back in and see if it works. So instead of two times X, it'll be two times one minus one. Under the square root bracket equals one. Let's keep simplifying the left side. So two times one. Well that's two minus one. And now we've got the square root of two minus one is one Equals one. And is that true? Well, yeah, it is because one could be written as one squared the square root of one squared, yep, that is equal to one. And now we can declare victory. That leaves us with answer choice. A well done. We'll catch you on the next one.

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