Baten80 wrote:

QR. 30 Number

If both x and y are nonzero numbers, what is the value of x/y?

(1) x = 6

(2) y^2 = x^2

I did wrong doing following:

√y^2 = √x^2

so, y=x

and answer c

What wrong did i do.

Note that \(\sqrt{x^2}=|x|\).

If both x and y are nonzero numbers, what is the value of x/y?(1) x = 6. Not sufficient.

(2) y^2 = x^2 --> \(|x|=|y|\) --> if \(x\) and \(y\) have the same sign then \(\frac{x}{y}=1\) (for example \(x=y=6\)) but if \(x\) and \(y\) have the opposite signs then \(\frac{x}{y}=-1\) (for example \(x=6\) and \(y=-6\)). Not sufficient.

(1)+(2) We still don't know whether \(x\) and \(y\) have the same sign or not. Not sufficient.

Answer: E.

About \(\sqrt{x^2}=|x|\).

The point here is that as

square root function can not give negative result then \(\sqrt{some \ expression}\geq{0}\).

So \(\sqrt{x^2}\geq{0}\). But what does \(\sqrt{x^2}\) equal to?

Let's consider following examples:

If \(x=5\) --> \(\sqrt{x^2}=\sqrt{25}=5=x=positive\);

If \(x=-5\) --> \(\sqrt{x^2}=\sqrt{25}=5=-x=positive\).

So we got that:

\(\sqrt{x^2}=x\), if \(x\geq{0}\);

\(\sqrt{x^2}=-x\), if \(x<0\).

What function does exactly the same thing? The absolute value function: \(|x|=x\), if \(x\geq{0}\) and \(|x|=-x\), if \(x<0\). That is why \(\sqrt{x^2}=|x|\).

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