Expert: Paul Klarreich - 10/9/2009

Question
I am having major trouble with the solutions hope you can help me. Please take a look at my attempts. Thanks!

3.For any numbers a and b, a*b = a + b - ab. If a*b = 0, which of the following CANNOT be a value of b?

a. 2
b.1
c.0
d.-1
e.-3/2

Again, I was completely stumped as to where to start with this question

4. This one is right angle triange where you have to use the Pythagorean Theorum (a squared + b squared = c squared)
It gives you that the hypotenuse is y miles and that the height is y/2 miles, the base is blank, so I call it x.  It also gives you that y squared is 2 (ie., it is telling us that the hypotenuse squared, aka c squared, is 2).  So I started to work it out and got stumped:

a^2 + b^2 = c^2

x^2 + (y/2)^2 = 2

Now I didn't know what the square root of 2 was, but I thought that I remembered a math rule that says half something and then square it, you end up with the base number - as if you never did anything to the number....so I figured that (y/2)^2 = y....so now I have:

x^2 + y = 2

But then I get stuck...I'm pretty sure my "math rule" is a dud, cause when I tried it out on a bunch of numbers, it only worked for the number 4... :(

I hope you have time to help me with these solutions!

Answer
Questioner: Daveena Harris
Country: United States
Category: Advanced Math
Private: Yes
Subject: Word Problems
Question: I am having major trouble with the solutions hope you can help me. Please take a look at my attempts. Thanks!
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Hi, Daveena,

It helps to know the context of these problems -- are you studying ninth-grade algebra?  What about Galois Theory?  Do you know what an integral domain is?  (My guess -- no.)
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3.For any numbers a and b, a*b = a + b - ab. If a*b = 0, which of the following CANNOT be a value of b?

a. 2
b.1
c.0
d.-1
e.-3/2

Again, I was completely stumped as to where to start with this question

Use some number facts, such as:

If  ab = 0, then either a = 0 or b = 0.  (a basic property of number systems used on the inner part of the galaxy -- Sorry, I've been watching too much Star Trek lately)

But it's true.
Now then, what do you mean by writing  a*b?  Do you mean the product?  If so, then what do you mean by writing  ab?  If that also means the product, then you have:

ab = a + b - ab

2ab = a + b

But  ab = 0, so  a + b = 0.  
However, if a = 0, then so is b.  Therefore you MUST have  b = 0.  Any of the values that isn't zero is no good.

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4. This one is right angle triange where you have to use the Pythagorean Theorum (a squared + b squared = c squared)
>> Yes, I have heard of it.

It gives you that the hypotenuse is y miles and that the height is y/2 miles, the base is blank, so I call it x.  It also gives you that y squared is 2 (ie., it is telling us that the hypotenuse squared, aka c squared, is 2).  So I started to work it out and got stumped:

a^2 + b^2 = c^2

x^2 + (y/2)^2 = 2

Now I didn't know what the square root of 2 was, but I thought that I remembered a math rule that says half something and then square it, you end up with the base number -

>> Huh?  Who told you that?  Your uncle?  Next time you see him, smile sweetly, tell him how smart he is, then forget anything he tells you.

as if you never did anything to the number....so I figured that (y/2)^2 = y....so now I have:

x^2 + y = 2

But then I get stuck...I'm pretty sure my "math rule" is a dud, cause when I tried it out on a bunch of numbers, it only worked for the number 4... :(

>> You are smart to check your assumptions. Good for you.


If y^2 = 2,  then  (y/2)^2 = y^2 / 4 = 2/4 = 1/2

x^2 + (y/2)^2 = 2   becomes:

x^2 + 1/2 = 2

x^2  = 3/2

x = sqrt(3/2)