Question

The sum of the squares of three different positive integers 2018, the largest number is the sum of the other two numbers, the difference between the two smaller numbers 2 Find the difference between the cubes of the two smaller numbers.

Answer 1

Step-by-step explanation:

Let k be the smallest number. Then the other small number is k+2, and the large number is 2k+2. So:

k²+(k+2)²+(2k+2)²=2018

k²+k²+4k+4+4k²+8k+4=2018

6k²+12k-2010=0

k²+2k-335=0

k=17.330302779823

k+2=19.330302779823

(k+2)³-k³=2018 ………………

Let k and k+2 be the smaller numbers, and 2k+2 be the larger number. Then the squares of the 3 positive numbers would be:

k²+(k+2)²+(2k+2)²=2018

k²+k²+4k+4+4k²+8k+4=2018

6k²+12k+8=2018

(k+2)³-(k)³=((k+2)-k)((k+2)²+((k)(k+2))+k²))

=(2)((k²+4k+4)+k²+2k+k²)

=(2)(3k²+6k+4)

=6k²+12k+8

Then:

6k²+12k+8=6k²+12k+8

So:

(k+2)³-k³=2018