Question

Ifa+b=5andasquar+bsqure=11then provethatacube+bcube=20

Answer 1

$<i>$Given -

a + b = 5

a² + b² = 11

Using formula

( a + b )² = a² + b² + 2ab

( 5 )² = 11 + 2ab

25 = 11 + 2ab

2ab = 25 - 11

2ab = 14

ab = 7

Now,

Again using identity

a³ + b³ = ( a + b ) ( a² + b² - ab )

R.H.S. = ( a + b ) ( a² + b² - ab )

= ( 5 ) ( 11 - 7 )

= 5 × 4

= 20

= L.H.S.

Hence verified.