Question

if a+b+c=3,a^2+b^2+c^2=5and a^3+b^3+c^3=9 find abc

Answer 1

Hi ,

It is given that ,

a + b + c = 3 ---- ( 1 )

a² + b² + c² = 5 ---( 2 )

a³ + b³ + c³ = 9 ---( 3 )

Do the square of equation ( 1 ) , we

get

( a + b + c )² = 3²

a² + b² + c² + 2( ab + bc + ca ) = 9

5 + 2( ab + bc + ca ) = 9

2 ( ab + bc + ca ) = 4

ab + bc + ca = 2 ---( 4 )

Now ,


By algebraic identity ,

a³ + b³ + c³ = ( a + b + c ) [ a²+b²+c²-(ab+bc+ca ] + 3abc

9 = 3 [ 5 - 2 ] + 3abc

9 = 3 × 3 + 3abc

9 - 9 = 3abc

0 = 3abc

Therefore ,

abc = 0

I hope this helps you.

: )