SOLUTION: I need help with a problem but cant type square root on my keyboard but I'll do my best, Here goes (X+1)^1/2+(2X)^1/2=1

Click here to see ALL problems on Square-cubic-other-roots

Question 101464: I need help with a problem but cant type square root on my keyboard but I'll do my best, Here goes (X+1)^1/2+(2X)^1/2=1
Found 2 solutions by stanbon, edjones:
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
(X+1)^1/2+(2X)^1/2=1
---------------------
(X+1)^1/2 = -(2X)^1/2+1
Square both sides:
x+1 = 2x+1 -2(2x)^(1/2)
x=2(2x)^(1/2)
Square both sides:
x^2 = 4(2x)
x^2-8x=0
x(x-8)=0
x=0 or x=8
-------------------
Check the answrs in (X+1)^1/2+(2X)^1/2=1
If x=0: sqrt(1)+ sqrt(0) = 1
True
-----------------
If x=8: sqrt(9)+sqrt(16)=1
False
--------------------
Only solution: x=0
==========================
Cheers,
Stan H.

Answer by edjones(8007) (Show Source):
You can put this solution on YOUR website!
sqrt(x+1)+sqrt(2x)=1
(sqrt(2x)-1)^2=(-sqrt(x+1))^2
2x-2sqrt(2x)+1=x+1
x=2sqrt(2x)
x^2=4*2x square both sides
x^2=8x
x^2-8x=0
x(x-8)=0 factor
x=0, x=8
Check:
sqrt(0+1)+sqrt(2*0)=1 true
sqrt(8+1)+sqrt(2*8)=1 false
.
x=0 is the only answer.
Ed