Question

If a + b + c = 6 and a^2+b^2+c^2=60,then find ab +bc+ca and a^3+b^3+c^3-3abc

Answer 1

Answer :-

→ -12 and 432 respectively .

Step-by-step explanation :-

We have,

→ a + b + c = 6 .

And, a² + b² + c² = 60 .

Now, using Identity :-)

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

→ ( 6 )² = 60 + 2( ab + bc + ca ) .

→ 36 = 60 + 2( ab + bc + ca ) .

→ 36 - 60 = 2( ab + bc + ca ) .

→ ab + bc + ca = -24/2 .

•°• ab + bc + ca = -12 .

Now, using Identity :-)

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

= ( 6 )[ 60 - ( -12 ) ] .

= ( 6 ) ( 60 + 12 ) .

= 6 × 72 .

•°• a³ + b³ + c³ - 3abc = 432 .

Hence, it is solved.