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.

GROUND RULE:

Never reduce equation by variable (or expression with variable), if you are not certain that variable (or expression with variable) doesn't equal to zero. We can not divide by zero.

Never multiply (or reduce) inequality by variable (or expression with variable) if you don't know the sign of it or are not certain that variable (or expression with variable) doesn't equal to zero.
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