Question

if a + b is equal to 5 and a square + b square is equal to 11 then prove that a cube plus b cube is equal to 20 Answer fast

Answer 1

Hey here is the answer in attachment.

Hence a^3 + b^3 = 20

Any doubts ask in comment

Tq

Answer 2

The proof is given below :

Given,

a + b = 5

Also,

a² + b² = 11

To prove :

a³ + b³ = 20

Proof :

Since we know,

a³ + b³ = ( a + b ) ( a² - ab + b² )

To find the value of  ' ab ' we will use formula :

( a + b ) ² = a² + b² + 2ab

Putting the values ,

( 5 ) ² = 11 + 2ab

25 = 11 + 2ab

25 - 11 = 2ab

14 = 2ab

Dividing both the sides by 2,

2ab / 2 = 14 / 2

ab = 7

Now,

a³ + b³ = ( a + b ) ( a² - ab + b² )

a³ + b³ = ( a + b ) ( a² + b² - ab  )

Putting the values,

a³ + b³ = ( 5 ) ( 11 - 7 )

a³ + b³ = ( 5 ) * 4

a³ + b³ = 20

Hence proved