Question

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

Answer 1

@zpupster could you help me with this one?

Answer 2

square both sides
what do you get?

Answer 3

hello?

Answer 4

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

Answer 5

Sorry I was away.

Answer 6

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

Answer 7

so 4 squared for the left side?

Answer 8

no lets square the right first what do you get?

Answer 9

1.4

Answer 10

think of it like this

((2x)^1/2)^2 multiply the exponents together

Answer 11

do you see it?

Answer 12

Ahh okay.

Answer 13

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

Answer 14

looks good!!