Question

The sum of the squares of two consecutive even integers is 1684. What are the integers?

Answer 1

To find the two consecutive even integers, set up an equation and solve it. The integers are 20 and 22.

Step-by-step explanation:

To find the two consecutive even integers, we can use algebraic expressions. Let's assume the smaller even integer is x. The next consecutive even integer would be x + 2. The sum of their squares is given as 1684, so we can write the equation:

x^2 + (x + 2)^2 = 1684

Expanding and simplifying the equation:

x^2 + x^2 + 4x + 4 = 1684

Combining like terms:

2x^2 + 4x + 4 - 1684 = 0

2x^2 + 4x - 1680 = 0

Dividing the equation by 2 to simplify:

x^2 + 2x - 840 = 0

We can solve this quadratic equation by factoring or using the quadratic formula. The two consecutive even integers are 20 and 22.

Answer 2

Step-by-step explanation:

Let the 2 consecutive integers be x and x+1.

x²+(x+1)²=1684

x²+(x+1)(x+1)=1684

x²+x²+x+x+1=1684

2x²+2x-1683=0

Using quadratic formular