Answer:
Step-by-step explanation:
Prove: That the sum of the squares of 4 consecutive integers is an even integer.
An integer is a any directed number that has no decimal part or indivisible fractional part. Examples are: 4, 100, 0, -20,-100 etc.
Selecting 4 consecutive positive integers: 5, 6, 7, 8. Then;
[tex]5^{2}[/tex] = 25
[tex]6^{2}[/tex] = 36
[tex]7^{2}[/tex] = 49
[tex]8^{2}[/tex] = 64
The sum of the squares = 25 + 36 + 49 + 64
= 174
Also,
Selecting 4 consecutive negative integers: -10, -11, -12, -13. Then;
[tex]-10^{2}[/tex] = 100
[tex]-11^{2}[/tex] = 121
[tex]-12^{2}[/tex] = 144
[tex]-13^{2}[/tex] = 169
The sum of the squares = 100 + 121 + 144 + 169
= 534
Therefore, the sum of the squares of 4 consecutive integers is an even integer.
