Question

What is the smallest number that can be added to 2018·2019·2020 so that the result of the addition is a perfect cube? Please answer soon!

Answer 1

`802`

Explanation:

`18^3=5832`

`19^3=6859`

`2018+2019+2020=6057`

`6859-6057=802`

Check.

`6057+802=6859`

`\sqrt[3]{6859} =19`

Answer 2

2019.

Explanation:

Let x = 2018, then x + 1 = 2019 and x + 2 = 2020.

x(x + 1)(x + 2)

= x(x^2 + 3x + 2)

= x^3 + 3x^2 + 2x ................(A)

Now the perfect cube of x + 1 is:

(x + 1)^3 = x^3 + 3x^2 + 3x + 1

If we add x + 1 to (A) we get this expression so the answer is x + 1

= 2019.