Explaining "If a=1 and b=1: then a squared - 1...

  • Thread starter Byrgg
  • Start date
In summary: In this case, it seems like the person was making a joke by showing how you can manipulate equations to get a false result. It's important to always be careful and critical when looking at equations and not just blindly accept them. In summary, the conversation focused on a mathematical equation that seemed to show that 2 was equal to 1. However, upon closer examination, it was revealed that the equation was manipulated in a way that led to a false result. It serves as a reminder to always be cautious and critical when dealing with equations.
  • #1
Byrgg
335
0
On another forum, someone had this in a sig:

If a=1 and b=1: then a squared - 1 = ab-b: then (a + 1)(a - 1) = b(a - 1):then a + 1 = b: thus 1 + 1 = 1: as a result 2 = 1

I couldn't follow all of it, could someone explain this to me?
 
Mathematics news on Phys.org
  • #2
In the step, (a+1)(a-1) = (b)(a-1), one "cancels" the a-1, which in this case in the same as cancelling zero on both sides. You can't cancel zero because, a.0 = b.0 doesn't necessarily mean that a = b.
 
  • #3
You couldn't follow the work or you don't understand why it works that way?

Here's the work:

a=b=1

a*a-1=a*b-b [since a=b=1]
(a+1)(a-1)=b(a-1) [factoring the right-hand side and factoring a b out of the left-hand side]
a+1=b dividing both sides by a-1
1+1=1
2=1

The problem is with the line I highlighted in red. You are dividing by a-1, but since a=1 you are actually dividing by zero, which is not defined.

Here's a simpler one to make it easier to see:

5*0=3*0
5=3 ["divide both sides by 0"] - obviously 5 does not equal 3.
 
  • #4
Oh, ok so they're telling lies sorry I forgot about the division by 0, now I have to go tell them how wrong they are. Thanks.
 
  • #5
There is a difference between a "lie" and a "joke".
 

FAQ: Explaining "If a=1 and b=1: then a squared - 1...

What does "a squared - 1" mean in the equation if a=1 and b=1?

"A squared - 1" is a mathematical expression that represents the result of squaring the value of a (multiplying it by itself) and then subtracting 1 from the result. In this equation, since a is equal to 1, the expression would be 1 squared - 1, which equals 0.

Can you explain why the value of a squared - 1 is 0 in this equation?

Since a is equal to 1, when we square it, we get 1 multiplied by 1, which equals 1. Then, when we subtract 1 from 1, we get 0. Therefore, the value of a squared - 1 is 0 in this equation.

How does the value of b affect the result of a squared - 1?

The value of b does not affect the result of a squared - 1 in this equation. Since b is not used in the expression, its value does not impact the final result. The only variable in the expression is a, which is equal to 1, resulting in a final value of 0.

What is the purpose of squaring a value in a mathematical equation?

Squaring a value means multiplying it by itself, and this is often done in mathematical equations to represent repeated operations or exponential growth. In this equation, a squared represents the value of a multiplied by itself, and it is then used in the expression to calculate the final result.

Can this equation be solved using different values for a and b?

Yes, this equation can be solved using different values for a and b. However, the result of a squared - 1 will vary depending on the values chosen for a and b. For example, if a=2 and b=3, then a squared - 1 would equal 3, since 2 squared is 4 and subtracting 1 from 4 gives us 3.

Similar threads

Replies
17
Views
688
Replies
41
Views
2K
Replies
2
Views
2K
Replies
9
Views
1K
Replies
1
Views
833
Replies
5
Views
873
Back
Top