The Sum Of The Squares Of Two Consecutive Even Integers 452.find The Intege…

the sum of the squares of two consecutive even integers 452.find the integers.

Answer:

Positive integers: 14 and 16

Negative integers: –16 and –14

Step-by-step explanation:

Let x be the 1st number

x + 2 be the 2nd number

x^2 + (x+2)^2 = 452

x^2 + x^2 + 4x + 4 = 452

2x^2 + 4x + 4 – 452 = 0

2x^2 + 4x – 448 = 0

Divide the whole equation by 2

x^2 + 2x – 224 = 0

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

x + 16 =0

x = -16

x-14=0

x = 14

when x = -16

x + 2= -16 + 2

x + 2 = -14

when x = 14

x + 2 = 14 + 2

x + 2 = 16

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