Solve and check for extraneous solutions.
√{x + √{2x} = √{2x}
Could you please show me the steps? Thanks a lot!

Question

Solve and check for extraneous solutions.
√{x + √{2x} = √{2x}
Could you please show me the steps? Thanks a lot!

anonymous · Answer

attachment

anonymous · Answer

@zpupster could you help me with this one?

zpupster · Answer

square both sides
what do you get?

zpupster · Answer

hello?

anonymous · Answer

so square each of the twos? 2 squared = 4.

anonymous · Answer

Sorry I was away.

zpupster · Answer

squaring both sides gets rid of the square root
but on the left  you have a square root inside a square root so we will have to do this process twice

anonymous · Answer

so 4 squared for the left side?

zpupster · Answer

no lets square the right first what do you get?

anonymous · Answer

1.4

zpupster · Answer

think of it like this

((2x)^1/2)^2  multiply the exponents together

zpupster · Answer

do you see it?

anonymous · Answer

Ahh okay.

anonymous · Answer

Does this look right?

65. √{2x} + x = 2x
√2x = x
2x = x^2
2x – x^2 = 0
-((-2 + x)x) = 0
(-2 + x = 0 
x = 2 or 0

@zpupster

zpupster · Answer

looks good!!