SOLUTION: Simplify √(3x + 4) - √(x+5) = 1

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Question 1192222: Simplify √(3x + 4) - √(x+5) = 1
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

sqrt%283x+%2B+4%29+-+sqrt%28x%2B5%29+=+1++
sqrt%28x+%2B+5%29+%2B+1+=+sqrt%283+x+%2B+4%29
%28sqrt%28x+%2B+5%29+%2B+1%29%5E2+=+%28sqrt%283+x+%2B+4%29%29%5E2
x+%2B+2sqrt%28x+%2B+5%29+%2B+6=3x+%2B+4
2sqrt%28x+%2B+5%29+=3x-x+%2B+4-6
2sqrt%28x+%2B+5%29+=2x+-2
sqrt%28x+%2B+5%29+=x+-1
%28sqrt%28x+%2B+5%29%29%5E2+=%28x+-1%29%5E2
x+%2B+5+=x%5E2+-2x%2B1
x%5E2+-2x%2B1-x-5=0
x%5E2+-3x-4=0
x%5E2+-3x-4=0
%28x+-+4%29+%28x+%2B+1%29+=+0

solutions:
x=4
x=-1
verify solutions:

sqrt%283%284%29+%2B+4%29+-+sqrt%284%2B5%29=1
sqrt%2816%29+-+sqrt%289%29=1+
4+-+3=1
1=1 ->true

sqrt%283%28-1%29+%2B+4%29+-+sqrt%28-1%2B5%29=1+
sqrt%281%29+-+sqrt%284%29=1+
1+-+2=1+
-1=1+-> not true=> so, x=-1 is not a solution

the solution is: x=4