Question

if a+b+c=9 and ab+bc ca= 23 then a^3+b^3+c^3 - 3abc is

Answer 1

Hi ,

It is given that ,

a + b + c = 9 ----( 1 )

ab + bc + ca = 23 ---( 2 )

Do the square of equation ( 1 ) , we get

( a + b + c )² = 9²

a² + b² + c² + 2( ab + bc + ca ) = 81


a² + b² + c² + 2 ( 23 ) = 81

a² + b² + c² + 46 = 81

a² + b² + c² = 81 - 46 = 35 ---( 3 )

NOW ,

a³ + b³ + c³ - 3abc

= ( a + b + c )[ a² + b² + c² - ( ab + bc + ca ) ]

= 9 [ 35 - 23 ]

= 9 × 12

= 108

I hope this helps you.

: )

Answer 2

Hi,

Please see the attached file!


Thanks