Question

If a + b= 12 and a b= 27, find the value of a 3 +b 3

Answer 1

Given:

a+b = 12

ab = 27

To find:

The value of a³ + b³

Solution:

We know that

a³ + b³ = (a + b)(a² +b² -ab)

Also,

(a + b)²= a² +b² + 2ab

=> a²+ b² = (a + b)²- 2ab

Now putting the value of a² + b²

We get,

a³ + b³ = (a+b){ [ (a+b)²-2ab ] -ab }

=> a³ + b³ = (a+b)[ (a+b)²-3ab ]

Putting the values

a³ + b³ = (12)[ (12)² - 3(27) ]

=> 12 (144 - 3×27)

=> 12 (144 - 81)

=> 12 × 63

=> 756

Hence, a³ + b³ = 756