The Product of two consecutive even integers is 224. Find the integers.

Question

I have no idea at this question.

Answer 1

Let first number = x

It's consecutive even integer is x+2.

Products of numbers is x(x+2)= x^2+2x

x^2+2x = 224

Subtract from each side by 224.

x^2+2x-224 = 0

x^2+16x-14x-224 = 0

x(x+16)-14(x+16) = 0

(x+16)(x-14) = 0

x+16 = 0

Subtract 16 from each side.

x = -16

and x-14 = 0

Add 14 to each side.

x = 14

If x = 14 then second integer x = 16

If x = -16 then second integer x = -14.