Question

if a+b=12and ab =27 find the value of a³+b³.​

Answer 1

Answer:-

a³ + b³ = 756

Given :-

a + b = 12

ab = 27

To find :-

The value of a³ + b³.

Solution:-

For solving this kind of question we need a suitable identity.

(a³ + b³) = (a + b) (a² + b² -ab)

Now, put the given value,

(a + b)² = a² + b² + 2ab

→(12)² = a² + b² + 2 × 27

→144 = a² + b² + 54

→a² + b² = 144 - 54

→a² + b² = 90

→(a³ + b³) = 12 ( 90 - 27)

→(a³ + b³) = 12 × 63

→a³ + b³ = 756

Some more identities:-

(a³ - b³) = (a - b) (a² + b² + ab)

( a + b)³ = a³ + b³ + 3ab ( a + b)

( a+ b)³ = a³ - b³ - 3ab ( a - b)

Answer 2

GIVEN :

a + b = 12

ab = 27

TO FIND :

a³ + b³

SOLUTION:

= a³ + b³

We know that,

a³ + b³ = (a + b)³ - 3ab (a + b)

= (12)³ - 3(27) (12)

= 1728 - 81 (12)

= 1728 - 972

= 756

Therefore, the value of a³ + b³ = 756.