Explain why the equation | x | = √x² has infinitely many solution...

Question

Explain why the equation | x | = √x² has infinitely many solutions.

Accepted Answer

Hello everyone in this video we're going to be looking at this practice problem where we want to find the number of solutions for the equation, absolute value of X plus two is equal to the square root of X plus two squared. So in this case we're trying to find all the solutions where the value that we plug into X makes this equation true. So first let's try to understand what this means or what each side means. So when I do the absolute value of X-plus two, that means that the inside of this absolute value B x plus two could either be positive X plus two Or negative x plus two because that absolute value will turn this negative positive. But that inside could still be negative. Well if I look at the right hand side, the square root of X plus two squared. That means that I could either have the square root of positive explains to Times positive X-plus two which would just give me positive X plus two. Or I could have the square root of negative X plus two times negative X plus two. Which would give me negative X plus two. You could also think of this as when you take the square root of a number, you will get plus or minus the inside. So that's just expressing it out. And if we look at the left hand side and the right hand side you can see that both of them have a positive X plus two and both of them have a negative X plus two. So that means that peace two sides are equal. So because both sides of the equation are equal, there will be infinitely many solutions because from negative infinity to positive infinity, these equations are equal to each other. So if we look at the answer choices, you can see that answer choice C also has infinitely many solutions, so that becomes our final answer for this problem. So hopefully this video helped and see you next time.

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Explain why the equation | x | = √x² has infinitely many solutions.

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