Why does 3√x = √x have two solutions?

[frozen7]

3(x)^1/2 = (x)^1/2

How come there are two answers for this equation?? 0 and 1/3

 

[siddharth]

Your equation is
$$3 \sqrt{x} = \sqrt {x}$$

How is 1/3 a solution?
On substituting 1/3 in the Left Hand side you get $$\sqrt 3$$

On substituting 1/3 in the Right Hand side you get $$\frac {1}{\sqrt 3}$$

So LHS is not equal to RHS.
This means that 1/3 is not a solution

 

[Phoenix314]

You should first square each side to get rid of the square root, giving you:

9x = x

And x = 0 should be your only answer

 

[Zurtex]

3(x)^1/2 = (x)^1/2

How come there are two answers for this equation?? 0 and 1/3

Erm:

$$3 \sqrt{x} = \sqrt{x}$$

$$3 \sqrt{x} - \sqrt{x} = 0$$

$$2 \sqrt{x} = 0$$

$$\sqrt{x} = 0$$

I think there is only one solution to that.

 

[Nylex]

You should first square each side to get rid of the square root, giving you:

9x = x

And x = 0 should be your only answer

You don't need to. It should be clear that x = 0, otherwise you'd have 3 = 1.