Sure, let's express \( 9^2 \) as the sum of two consecutive integers.
First, calculate \( 9^2 \):
[tex]\[ 9^2 = 81 \][/tex]
Let's denote the two consecutive integers as \( x \) and \( x + 1 \). According to the problem, their sum should equal 81. Therefore, we can write:
[tex]\[ x + (x + 1) = 81 \][/tex]
Simplify this equation:
[tex]\[ x + x + 1 = 81 \][/tex]
[tex]\[ 2x + 1 = 81 \][/tex]
Next, we need to solve for \( x \). Subtract 1 from both sides of the equation:
[tex]\[ 2x = 80 \][/tex]
Now, divide both sides by 2:
[tex]\[ x = 40 \][/tex]
So, the two consecutive integers are \( x = 40 \) and \( x + 1 = 41 \).
Therefore, \( 9^2 \) can be expressed as the sum of the two consecutive integers 40 and 41.
So, the solution is:
[tex]\[ 81 = 40 + 41 \][/tex]
