The sum of the squares of two positive consecutive is 41. Find the integers.

16+25=41, so ...

To solve this problem, we need to set up equations based on the given information and use algebraic methods to find the solution. Let's represent the first positive integer as "x" and the second positive integer as "x + 1."

According to the problem, the sum of the squares of these two consecutive integers is 41. So we can set up an equation:

x^2 + (x + 1)^2 = 41

Expanding the equation, we get:

x^2 + x^2 + 2x + 1 = 41

Combining like terms:

2x^2 + 2x + 1 = 41

Rearranging the terms:

2x^2 + 2x - 40 = 0

Dividing the entire equation by 2 to simplify:

x^2 + x - 20 = 0

Now we need to solve this quadratic equation. We can factor it or use the quadratic formula to find the solutions. Let's use factoring:

(x + 5)(x - 4) = 0

Setting each factor to zero:

x + 5 = 0 or x - 4 = 0

Solving for x:

x = -5 or x = 4

Since we are looking for positive consecutive integers, we discard the negative solution. Therefore, the first positive integer is 4, and the second positive integer is 4 + 1 = 5.

Hence, the two positive consecutive integers are 4 and 5.