Question 152752
Solve for all values of x: square root sign (x+7) - square root sign (x+2)=1 
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{{{sqrt(x+7) - sqrt(x+2)}}} = 1
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{{{sqrt(x+7) = sqrt(x+2)}}} + 1; add {{{sqrt(x+2)}}} to both sides
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x + 7 = (x+2) + {{{2sqrt(x+2)}}} + 1; Square both sides, (FOIL the right side)
:
x + 7 = x + 3 + {{{2sqrt(x+2)}}} 
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x - x + 7 - 3 = {{{2sqrt(x+2)}}}
:
4 = {{{2sqrt(x+2)}}}
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16 = 4(x+2); squared both sides, gets rid of the 2nd radical
:
16 = 4x + 8
:
16 - 8 = 4x
x = {{{8/4}}}
x = 2
:
:
Check solution in original equation:
{{{sqrt(2+7) - sqrt(2+2)}}} = 1
{{{sqrt(9) - sqrt(4)}}} = 1; confirms our solution
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