- #1

- 21

- 0

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.

- Thread starter yoyo
- Start date

- #1

- 21

- 0

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.

- #2

- 441

- 0

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

...

- #3

- 21

- 0

oh i see what you are saying. Silly mistake on me. Thank you so much!