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Warning: Many instructors do not to show many examples (in class or in the homework) of radical equations for which the solutions don't actually work.But then they'll put one or more of these on the next test.But I'll check my solution at the end, anyway, because the instructions require it.
(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".
If the instructions don't tell you that you must check your answers, check them anyway.
At the very least, compare your solution with a graph on your graphing calculator.
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".
(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.
On the left-hand side of this equation, I have a square root. On the right-hand side, I've got a positive number.
Since both sides are known positive, squaring won't introduce extraneous solutions.