SOLUTION: √5x+1 +√x+1 =√10x+6

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Question 1131612: √5x+1 +√x+1 =√10x+6
Found 2 solutions by MathLover1, ikleyn:
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

sqrt%285x%2B1%29+%2Bsqrt%28x%2B1%29+=sqrt%2810x%2B6+%29....square both sides

%28sqrt%285x%2B1%29+%2Bsqrt%28x%2B1%29+%29%5E2=%28sqrt%2810x%2B6+%29%29%5E2



5x%2B1%2B2sqrt%285x%2B1%29+%2Asqrt%28x%2B1%29%2Bx%2B1=10x%2B6+

6x%2B2%2B2sqrt%28%285x%2B1%29+%28x%2B1%29%29=10x%2B6+

2sqrt%28%285x%2B1%29+%28x%2B1%29%29=10x-6x%2B6+-2

2sqrt%28%285x%2B1%29+%28x%2B1%29%29=4x%2B4

sqrt%28%285x%2B1%29+%28x%2B1%29%29=4x%2F2%2B4%2F2

sqrt%28%285x%2B1%29+%28x%2B1%29%29=2x%2B2....square both sides

%28sqrt%28%285x%2B1%29+%28x%2B1%29%29%29%5E2=%282x%2B2%29%5E2

%285x%2B1%29+%28x%2B1%29=4x%5E2%2B8x%2B4

5x%5E2+%2B+6+x+%2B+1=4x%5E2%2B8x%2B4

5x%5E2+%2B+6+x+%2B+1-4x%5E2-8x-4=0

x%5E2+-2x-3=0...factor

x%5E2+%2Bx-3x-3=0

%28x%5E2+%2Bx%29-%283x%2B3%29=0

x%28x+%2B1%29-3%28x%2B1%29=0

%28x-3%29%28x%2B1%29=0

solutions:
x=3
x=-1


Answer by ikleyn(52779) About Me  (Show Source):
You can put this solution on YOUR website!
.
The correct answer is x= 3.

x= -1 is not the solution in the real domain, since otherwise you will have a negative number under the square root.