Why is this wrong (II) ?

[AvgStudent]

$$-6=-6\\ 4-10=9-15\\ 4-10+\frac{25}{4}=9-15+\frac{25}{4}\\ 2^2-2(2)\left(\frac{5}{2}\right) +\left(\frac{5}{2}\right)^2=3^2-2(3)\left(\frac{5}{2}\right) +\left(\frac{5}{2}\right)^2\\ \left(2-\frac{5}{2}\right)^2=\left(3-\frac{5}{2}\right)^2\\ 2-\frac{5}{2}=3-\frac{5}{2}\\ 2=3$$

 

[Dr.Peterson]

Please do some thinking for yourself. Have you followed each step to see at what point the equation is false? Have you considered what sort of mistakes one might make?

The point of an exercise like this (in part) is to give you practice in catching your own errors, not in asking someone else to find them.

 

[AvgStudent]

It took me a while, but I figured it out. The second to last line is wrong because you take the square root of a negative value on the left-hand side.

 

[topsquark]

It took me a while, but I figured it out. The second to last line is wrong because you take the square root of a negative value on the left-hand side.

Not quite. You are taking the square root of a positive number so that's fine. The problem is that when you take the square root you could get an answer that is negative. For example
$$\sqrt{ \left ( 2 - \dfrac{5}{2} \right ) ^2} = \pm \left ( 2 - \dfrac{5}{2} \right )$$and it is the negative sign that is correct in this case.

-Dan

 

[AvgStudent]

Not quite. You are taking the square root of a positive number so that's fine. The problem is that when you take the square root you could get an answer that is negative. For example
$$\sqrt{ \left ( 2 - \dfrac{5}{2} \right ) ^2} = \pm \left ( 2 - \dfrac{5}{2} \right )$$and it is the negative sign that is correct in this case.

-Dan

Thanks. Makes sense.

 

[Dr.Peterson]

Not quite. You are taking the square root of a positive number so that's fine. The problem is that when you take the square root you could get an answer that is negative. For example
$$\sqrt{ \left ( 2 - \dfrac{5}{2} \right ) ^2} = \pm \left ( 2 - \dfrac{5}{2} \right )$$and it is the negative sign that is correct in this case.

-Dan

An alternative way to say this is that when you take the square root of a square, the result is really the absolute value: $\sqrt{x^2}=|x|$. So the next to last line should be $$\left | 2 - \dfrac{5}{2} \right | = \left | 3 - \dfrac{5}{2} \right |$$ which is still true.

 

[AvgStudent]

An alternative way to say this is that when you take the square root of a square, the result is really the absolute value: $\sqrt{x^2}=|x|$. So the next to last line should be $$\left | 2 - \dfrac{5}{2} \right | = \left | 3 - \dfrac{5}{2} \right |$$ which is still true.

Learned something new. Thanks, @Dr.Peterson. Adding that to my math reservoir.

 

[Steven G]

It took me a while, but I figured it out. The second to last line is wrong because you take the square root of a negative value on the left-hand side.

That line has on the left hand side something being squared and something being squared to the right hand side. None of these quantities are negative, so why are you saying that you are taking the square root of a negative number? You logic is flawed.

 

[AvgStudent]

That line has on the left hand side something being squared and something being squared to the right hand side. None of these quantities are negative, so why are you saying that you are taking the square root of a negative number? You logic is flawed.

I've acknowledged my logic is flawed through my replies above.