Question

a+b+c=5 and ab+bc+ca= 10 then prove that a^3+b^3+c^3_3abc=_25

Answer 1

Hi ,

a + b + c = 5 ---( 1 )

ab + bc + ca = 10 ---( 2 )

Do the square of equation ( 1 ) , we get

( a + b + c )² = 5²

a² + b² + c² + 2( ab + bc + ca ) = 25

a² + b² + c² + 2 × 10 = 25 [ from ( 2 ) ]

a² + b² + c² = 25 - 20 = 5 ----( 3 )

Now

a³ + b³ + c³

= ( a + b + c )[ a² + b² + c²-(ab + bc + ca)] +3abc

= 5 × ( 5 - 10 ) + 3abc

= 5 × ( - 5 ) + 3abc

= 3abc - 25


Hence proved.

I hope this helps you.

: )

Answer 2

Hi,

Please see the attached file!

Thanks