For all positive integers x, let x▲ be defined to be (x-1)(x+1). Which of the following is equal to 6▲ - 5▲ ?
Does this mean I'm supposed to multiply the 6 and the 5 to (x^2-1) and subtract them from each other?
Well, I guess you could say that! But isn't it more fun to think of it as performing a magic trick on those numbers? Let's see:
First, let's calculate 6▲. We take 6, subtract 1, and then multiply by 6+1. So, 6▲ is equal to (6-1)(6+1) = 5 * 7 = 35.
Now, let's calculate 5▲. We take 5, subtract 1, and then multiply by 5+1. So, 5▲ is equal to (5-1)(5+1) = 4 * 6 = 24.
Finally, let's subtract 5▲ from 6▲. We have 35 - 24 = 11.
So, 6▲ - 5▲ is equal to 11. Ta-da!
Yes, you are correct. To find the value of 6▲ - 5▲, you will multiply both 6 and 5 by the expression (x-1)(x+1), and then subtract the results from each other.
So, let's calculate it step-by-step:
Step 1: Find the value of 6▲.
Substitute x = 6 into the expression (x-1)(x+1):
6▲ = (6-1)(6+1)
= 5 * 7
= 35
Step 2: Find the value of 5▲.
Substitute x = 5 into the expression (x-1)(x+1):
5▲ = (5-1)(5+1)
= 4 * 6
= 24
Step 3: Evaluate the expression 6▲ - 5▲.
6▲ - 5▲ = 35 - 24
= 11
Therefore, 6▲ - 5▲ is equal to 11.
To find the value of 6▲ - 5▲, we first need to understand the definition of x▲. The given definition states that x▲ is equal to (x-1)(x+1).
Now let's substitute the values of 6 and 5 into the definition to get the expressions for 6▲ and 5▲:
- 6▲ = (6-1)(6+1) = 5*7 = 35
- 5▲ = (5-1)(5+1) = 4*6 = 24
Therefore, 6▲ - 5▲ can be calculated as:
35 - 24 = 11
So, the answer is 11.
x▲ = (x-1)(x+1)
then
6▲ - 5▲
= (6-1)(6+1) - (5-1)(5+1)
= 35 - 24
= 11
11 should be one of your choices
or the way you did it:
x▲ = (x-1)(x+1) = x^2 - 1
6▲ = 36-1 = 35
5▲ = 24-1 = 24
as above