The two consecutive even integers are 20, 22 and -20, -22
"An integer is a whole number from the set of negative and positive numbers. "
Integers: - . . ., -2, -1 , 0, 1, 2, . . .
"Any number that can be exactly divided by 2."
For given situation,
we have been given that the sum of the squares of two consecutive even integers is 884.
Let, x and (x + 2) are two consecutive even numbers.
The sum of square of these numbers would be,
= [tex]x^2 + (x+2)^2[/tex]
= [tex]x^2 + (x^2 + 2(2)(x) + 2^2)[/tex]
= [tex]x^2+(x^2+4x+4)[/tex]
= [tex]2x^2+4x+4[/tex]
Since, the sum of the squares of two consecutive even integers is 884.
⇒ [tex]x^2 + (x+2)^2=884[/tex]
⇒ [tex]2x^2+4x+4=884[/tex]
⇒ [tex]2(x^2+2x+2)=442[/tex]
⇒ [tex]x^2+2x+2=442[/tex]
⇒ [tex]x^2+2x+2-442=442-442[/tex]
⇒ [tex]x^2+2x-440=0[/tex]
⇒ [tex]x^2+22x-20x-440=0[/tex]
⇒ [tex](x+22)(x-20)=0[/tex]
⇒ x + 22 = 0 or x - 20 = 0
⇒ x = -22 or x = 20
For x = -22,
⇒ x + 2 = -20
For x = 20,
⇒ x + 2 = 22
Therefore, the integers are ±20 and ±22.
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