SOLUTION: If x to the second= x to the third, give the two possible values for x

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Question 96414This question is from textbook McDougal Littel Middle School Math
: If x to the second= x to the third, give the two possible values for xThis question is from textbook McDougal Littel Middle School Math

Answer by bucky(2097) About Me  (Show Source):
You can put this solution on YOUR website!
Given:
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x%5E2+=+x%5E3
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Let's transpose this just to reverse the sides and get:
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x%5E3+=+x%5E2
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Subtract x%5E2 from both sides:
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x%5E3+-+x%5E2+=+0
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Now factor x%5E2 from both terms on the left side to get:
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x%5E2%2A%28x+-+1%29+=+0
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This equation will be true if either factor on the left side is zero because multiplication
by a zero on the left side makes the entire left side equal to zero and therefore equal
to the right side.
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So we can say that either x%5E2+=+0 or x+-+1=+0 will result in the equation being
satisfied.
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To have x%5E2+=+0 you must have x equal zero.
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And to have x+-+1+=+0 add 1 to both sides and you get x+=+1
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So the two solutions to this problem are x = 1 and x = 0.
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If you put each of these answers into the original equation x%5E2+=+x%5E3 you will see
that the left side equals the right side. When x equals zero the equation becomes
0 = 0 and when x = 1 the equation becomes 1 = 1. So both 0 and 1 check as answers to
the problem.
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Hope this helps you to understand the problem and how you can get a solution.
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