Rewrite an Expression to Eliminate Absolute Value

[nycmathguy]

Homework Statement

Rewrite an expression to eliminate absolute value.

Relevant Equations

n/a

See attachment.

I don't understand the solution given by David Cohen.

1. Note: x^2 is nonnegative for any real number x. This is because any value for x when squared is positive. Yes?

2. If x is greater than or equal to 0, then I can say that -2 - x^2 is negative in value, right?

3. What is David Cohen really trying to explain here?

 

[Mark44]

Homework Statement:: Rewrite an expression to eliminate absolute value.
Relevant Equations:: n/a

See attachment.

I don't understand the solution given by David Cohen.

1. Note: x^2 is nonnegative for any real number x. This is because any value for x when squared is positive. Yes?

Yes

2. If x is greater than or equal to 0, then I can say that -2 - x^2 is negative in value, right?

And you can say the same thing if $x < 0$.

3. What is David Cohen really trying to explain here?

That $|-2 - x^2| = 2 + x^2$

Taking this further, it's easy to see that $|-2 - x^2| \ge 2$.

 

[nycmathguy]

Yes
And you can say the same thing if $x < 0$.
That $|-2 - x^2| = 2 + x^2$

Taking this further, it's easy to see that $|-2 - x^2| \ge 2$.

Sorry but I don't understand what you're saying.

 

[Delta2]

$-2-x^2$ is negative for any real number x.
Hence by definition of absolute value it will be $|-2-x^2|=-(-2-x^2)$ and after that it is algebra 1 process to show that$-(-2-x^2)=2+x^2$ (can give you the detailed in between algebra 1 steps if you are interested).

 

[Delta2]

Setting $y=-2-x^2$ we know that y<0 for any x, hence by definition of absolute value $|y|=-y$ in case you are wondering how we apply the definition in this case.

 

[nycmathguy]

Thank you.

 

[nycmathguy]

I think the time has come for me to reconsider why I joined this site. Maybe I will leave.

 

[Delta2]

I think the time has come for me to reconsider why I joined this site. Maybe I will leave.

Why is that, the only thing I find wrong with you is that you post multiples of similar problems, my guess is that you do it in order to be absolutely sure that you got it right.

 

[nycmathguy]

Why is that, the only thing I find wrong with you is that you post multiples of similar problems, my guess is that you do it in order to be absolutely sure that you got it right.

I am just thinking about it. I post multiple problems to get additional practice.

 

[Delta2]

I would recommend you not to leave. Even if some really good science advisors-homework helpers have unfriendly attitude towards you, and probably not willing to help you in the future, we can travel the road without them and see how it goes. I hope it goes well!

[Post edited by a Mentor]

 

[MidgetDwarf]

In general. Think of the absolute value as a function (well it is), that is piecewise-defined.

Ie., |y| = y, if y≥ 0 or |y| = - y , if y<0.

So when ever you see the absolute value function in a problem, you should think about both cases.
However, with the problem you listed, we know that the square of any number is positive, and the sum of two positive numbers is positive...

 

[nycmathguy]

In general. Think of the absolute value as a function (well it is), that is piecewise-defined.

Ie., |y| = y, if y≥ 0 or |y| = - y , if y<0.

So when ever you see the absolute value function in a problem, you should think about both cases.
However, with the problem you listed, we know that the square of any number is positive, and the sum of two positive numbers is positive...

Thank you everyone.