SOLUTION: Solve for all values of x: square root sign (x+7) - square root sign (x+2)=1 I am not sure what to do with this question. I think maybe I should mutilply by x+7 and x+5 to remo

Algebra ->  Radicals -> SOLUTION: Solve for all values of x: square root sign (x+7) - square root sign (x+2)=1 I am not sure what to do with this question. I think maybe I should mutilply by x+7 and x+5 to remo      Log On


   

Question 152752: Solve for all values of x: square root sign (x+7) - square root sign (x+2)=1
I am not sure what to do with this question. I think maybe I should mutilply by x+7 and x+5 to remove the square root sign, but then I am lost
Thanks
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Solve for all values of x: square root sign (x+7) - square root sign (x+2)=1
;
sqrt%28x%2B7%29+-+sqrt%28x%2B2%29 = 1
:
sqrt%28x%2B7%29+=+sqrt%28x%2B2%29 + 1; add sqrt%28x%2B2%29 to both sides
:
x + 7 = (x+2) + 2sqrt%28x%2B2%29 + 1; Square both sides, (FOIL the right side)
:
x + 7 = x + 3 + 2sqrt%28x%2B2%29
:
x - x + 7 - 3 = 2sqrt%28x%2B2%29
:
4 = 2sqrt%28x%2B2%29
:
16 = 4(x+2); squared both sides, gets rid of the 2nd radical
:
16 = 4x + 8
:
16 - 8 = 4x
x = 8%2F4
x = 2
:
:
Check solution in original equation:
sqrt%282%2B7%29+-+sqrt%282%2B2%29 = 1
sqrt%289%29+-+sqrt%284%29 = 1; confirms our solution
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