Solving for X involving Square Roots

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SUMMARY

The discussion centers on solving the equation sqrt(x+9) - sqrt(x-6) = 3, with the confirmed solution x=7. The user initially struggled with demonstrating the solution algebraically and expressed frustration over the cancellation of x when squaring both sides. The correct approach involves squaring the equation, leading to the expression 2x + 3 - 2*sqrt((x+9)(x-6)) = 9, which clarifies the steps to isolate x.

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Students learning algebra, educators teaching mathematical concepts, and anyone looking to improve their problem-solving skills in equations involving square roots.

yoyo
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Hi, I am getting frustrated with trying to solve this equation:

sqrt(x+9) - sqrt(x-6) = 3.

I know that the answer is x=7 because of guess and check. I don't know how to show it algebraically. Squaring both sides will cancel out the x. Is there a trick or something this? Please help. Thanks in advance.
 
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Can you show how squaring both sides cancels out the x?

If I square both sides I get:

(sqrt(x+9) - sqrt (x-6))^2 = 3^2

x+9 - 2*sqrt(x+9)*sqrt(x-6) + x - 6 = 9

2x + 3 - 2*sqrt((x+9)(x-6)) = 9
...
 
oh i see what you are saying. Silly mistake on me. Thank you so much!
 

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