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Unformatted text preview: ossibility here is that we made a mistake somewhere. We
can go back and look however and we’ll quickly see that we haven’t made a mistake.
So, what is the deal? Remember that our first step in the solution process was to square both
sides. Notice that if we plug x = -2 into the quadratic we solved it would in fact be a solution to
that. When we squared both sides of the equation we actually changed the equation and in the
process introduced a solution that is not a solution to the original equation.
With these problems it is vitally important that you check your solutions as this will often happen.
When this does we only take the values that are actual solutions to the original equation.
So, the original equation had a single solution x = 3 .
Now, as this example has shown us, we have to be very careful in solving these equations. When
we solve the quadratic we will get two solutions and it is possible both of these, one of these, or
none of these values to be solutions to the original equation. The only way to know is to check
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This note was uploaded on 06/06/2012 for the course ICT 4 taught by Professor Mrvinh during the Spring '12 term at Hanoi University of Technology.
- Spring '12