Pedros wrote:

what is the value of x?

1) 6x=√(3x)

2) x>0

OA :

thanks

(1) Square both sides --> \(36x^2=3x\) --> \(12x^2=x\), NOTE that here we can not reduce by \(x\), as we don't know the value of \(x\). Meaning that \(x\) can be zero and if so we can not reduce (divide) by zero --> \(x(12x-1)=0\) --> \(x=0\) OR \(x=\frac{1}{12}\). Two possible values for \(x\), not sufficient.

(2) \(x>0\), clearly not sufficient.

(1)+(2) \(x=0\) OR \(x=\frac{1}{12}\) BUT \(x>0\), \(x\) can not be zero, so \(x=\frac{1}{12}\). Sufficient.

Answer: C.

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