# Radical Equations And Problem Solving (Yes, this means that you can use your graphing calculator to help you check your work.) When I was solving " lines had not intersected.This illustrates why I had to check my solution to figure out that the real answer was "no solution".

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So I'd have been checking my solutions for this question, even if they hadn't told me to.

I'll treat the two sides of this equation as two functions, and graph them, so I have some idea what to expect. This is for my own sense of confidence in my work.) I'll graph the two sides of the equation as: solution. It came from my squaring both sides of the original equation. I can see it in the squared functions and their graph: ("Extraneous", pronounced as "eck-STRAY-nee-uss", in this context means "mathematically correct, but not relevant or useful, as far as the original question is concerned".

The left-hand side of the equation can be graphed as one curve, and the right-hand side of the equation can be graphed as another curve.

The solution to the original equation is the intersection of the two curves.

(This is just one of many potential errors possible in mathematics.) To see how this works in our current context, let's look at a very simple radical equation: There is another way to look at this "no solution" difficulty.

When we are solving an equation, we can view the process as trying to find where two lines intersect on a graph.

For instance, in my first example above, " Squaring both sides of an equation is an "irreversible" step, in the sense that, having taken the step, we can't necessarily go back to what we'd started with.

By squaring, we may have lost some of the original information.

But you have to be very careful there because when you square radical signs you actually lose the information that you were taking the principal square root. So the first thing I want to do is I want to isolate this on one side of the equation.

Not the negative square root or not the plus or minus square root. And so when we get our final answer, we do have to check and make sure that it gels with taking the principal square root. And the best way to isolate that is to get rid of this 3.