Question

If a,b,c are real numbers such that a+b+c =7 ,a2+b2+c2=35 ,a3+b3+c3=151 then value of abc

Answer 1

Hello friends!!

Here is ur answer :

Given :

a + b + c = 7

a² + b² + c² = 35

a³ + b³ + c³ = 151

To find :

abc

Solution :

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

a³ + b³ + c³ - 3abc = ( a + b + c ) ( a² + b² + c² - (ab + bc + ca) ) - - - - - - - ( 1 )

First we have to find the value of ab + bc + ca

Using identity,

( a + b + c )² = a² + b²+ c² + 2 ( ab + bc + ca )

Putting the values

( 7 )² = 35 + 2 ( ab + bc + ca )

49 = 35 + 2 ( ab + bc + ca )

2( ab + bc + ca ) = 49 - 35

ab + bc + ca = 14 / 2

ab + bc + ca = 7

Put the value of Ab + bc + ca in eqⁿ ( 1 )

151 - 3(abc) = ( 7 ) ( 35 - 7 )

151 - 3 ( abc) = 7 × 28

151 - 3 ( abc) = 196

- 3 ( abc ) = 196 - 151

- 3 ( abc ) = 45

abc = - 45/3

abc = - 15

HOPE IT HELPS YOU...