Algebra Review

[armeeta2002]

We're starting trig. soon so our teacher decided to "toughen us up" by giving us algebra reviews.

Basically, this is what the worksheet reads:
Each condition given below is true in some cases and false in at least one instance. For each numbered item, give one example that shows when the condition is true and one that shows when it is false. Your answer many take the form of a diagram, and expression, and equation, or a written response.


1. If a^2 = b^2, then a=b. List the true and false examples.

So far I've tried plugging in numbers into the equation , but then i realized if a=b then it would have to be the same number, however they are two different variables which confused me.

---
2. x^y = y^x for whole numbers x and y


---
3. ([sqrt] a+b) = [sqrt]a + [sqrt]b


These are the only three I don't understand on the worksheet.

Can someone explain it?

 

[pka]

1. If a^2 = b^2, then a=b. List the true and false examples.
Let a=-2 and b=2
---
2. x^y = y^x for whole numbers x and y
Let x=2 and y=-1

---
3. ([sqrt] a+b) = [sqrt]a + [sqrt]b
Let a=2 and b=2

 

[armeeta2002]

That makes sense...Can someone explain a square trinomial?

The problem states ax^2 +bx +c is a square trinomial.

 

[tkhunny]

Your teacher is wise to force you to do an algebra review. You probably wouldn't do it, otherwise. You WILL need it, particularly if this question is any indication.

It makes very little sense to call a*x^2 + b*x + c a square trinomial. It is a generalized trinomial that could have any properties whatsoever. A SQUARE trinomial is one that can be rewritten as (a*x+b)^2, producing \(\displaystyle a^{2}x^{2}\;+\;2*(a+b)*x\;+\;c^{2}\). In other words, it will be a square trinomial, a*x^2 + b*x + c IF (a really big IF) 'a' and 'c' are perfect squares and 'b' is twice the sum of their square roots. You'ld beter reread the section and make sure you get it straight.