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

frozen7

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

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

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siddharth

Homework Helper
Gold Member
$$3 \sqrt{x} = \sqrt {x}$$

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

Homework Helper
frozen7 said:
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

Phoenix314 said:
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.

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