Question

Write the value of 30³ + 20³ − 50³.

Answer 1

The given expression is

 30³ + 20³ − 50³.

Let a=30,b= 20  and c = - 50. Then the given expression becomes

 `30^3 + 20^3 - 50^3 = a^3 +b^3 + c^3`

Note that

`a+b+c = 30 + 20 + (-50)`

                 ` =30 + 20 - 50`

                  ` =0`

Recall the formula

`a^3 + b^3 +c^3 - 3abc = (a+b+c)(a^2 +b^2 + c^2 - ab - bc - ca)`

When a + b + c = 0, this becomes

`a^3 +b^3 + c^3  - 3abc = 0.(a^2 + b^2 +c^2 - ab - bc - ca)`

 `a^3 +b^3+c^3 = 3abc`

So, we have the new formula

 `a^3 +b^3+c^3 = 3abc` , when a + b + c = 0,.

Using the above formula, the value of the given expression is

 `a^3 +b^3+c^3 = 3abc`

 `30^3 + 20^3 - 50^3 = 3.(30).(20).( -50)`

 `30^3 + 20^3 - 50^3 = -90000`