SOLUTION: square root of x-4 minus the square root of x-7 = 1

Question 121736: square root of x-4 minus the square root of x-7 = 1
Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
Given:
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To make it easier to solve for x, let's begin by taking one of the radicals to the other side.
We can get rid of the on the left side by adding to both
sides. On the left side this addition cancels out the and the equation
then becomes:
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Now square both sides. If you do that the equation becomes:
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Let's next get rid of the terms that are just "x" on both sides by subtracting x from both
sides and the equation reduces to:
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On the right side combine the 1 and the -7 to get -6, making the equation:
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Get rid of the -6 on the right side by adding +6 to both sides to further reduce the equation to:
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Divide both sides of the equation by 2 to get rid of the "2s" and the equation is then:
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Again, square both sides and the equation then is:
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Get rid of the -7 on the right side by adding 7 to both sides and you finally have:
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So the answer is x = 8. Let's check it, just to make sure. Return to the original given
equation:
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Substitute 8 for x and the original equation becomes:
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Simplify the numbers under the radicals and you have:
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This simplifies to:
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The left side equals the right side so the answer checks out OK. Our answer of x = 8 is correct.
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Hope this helps you to see your way through the problem.
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