Question

If a+b=5 and a square+bsquare=11 then prove that acube+b cube=20

Answer 1

this is ur correct answer

Answer 2

Answer:

The proof is given below :

Step-by-step explanation:

Given,

a + b = 5

a² + b² = 11

Now we know,

( a + b )² = a² + b² + 2ab

Substituting the value of ( a + b ) and a² + b²

( 5 )² = 11 + 2ab

25 = 11 + 2ab

25 - 11 = 2ab

2ab = 14

Dividing both sides by 2,

2ab / 2 = 14 / 2

ab = 7

Now,

a³ + b³ = ( a + b ) ( a² -ab + b² )

a³ + b³ = ( a + b ) ( a² + b² - ab )

Substituting the values,

a³ + b³ = ( 5 ) ( 11 - 7 )

a³ + b³ = ( 5 ) ( 4 )

a³ + b³ = 20

Hence,

Proved that if a+b=5 and a^2+b^2=11 then a^3+b^3=20