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Unformatted text preview: ough here is set up to eliminate the square
root. However, as we will see, the steps that we’re going to take can actually cause problems for
us. So, let’s see how this all works.
Let’s notice that if we just square both sides we can make the square root go away. Let’s do that
and see what happens. ( x) 2 = ( x+6 ) 2 x2 = x + 6
x2 - x - 6 = 0 ( x - 3)( x + 2 ) = 0 Þ x = 3, x = -2 Upon squaring both sides we see that we get a factorable quadratic equation that gives us two
solutions x = 3 and x = -2 .
Now, for no apparent reason, let’s do something that we haven’t actually done since the section
on solving linear equations. Let’s check our answers. Remember as well that we need to check
the answers in the original equation! That is very important.
Let’s first check x = 3
? 3= 3 + 6
3= 9 OK So x = 3 is a solution. Now let’s check x = -2 . © 2007 Paul Dawkins 116 http://tutorial.math.lamar.edu/terms.aspx College Algebra ? -2 = -2 + 6
-2 ¹ 4 = 2 NOT OK We have a problem. Recall that square roots are ALWAYS positive and so x = -2 does not
work in the original equation. One p...
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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