Question

If a + b + c = 15, and a2 + b2 + c2 = 83, find ab + bc + ca.

Answer 1

Given:-)

→ a + b + c = 15.

→ a² + b² + c² = 83.

To Find:-)

→ a³ + b³ + c³ - 3abc.

Solution:-)

▶We have,

=> a + b + c = 15.

[ Squaring both side ].

=> ( a + b + c )² = ( 15 )².

=> a² + b² + c² + 2( ab + bc + ca ) = 225.

=> 83 + 2( ab + bc + ca ) = 225.

=> 2( ab + bc + ca ) = 225 - 83.

= > ab + bc + ca = \frac{142}{2} .=>ab+bc+ca=

2

142

.

=> ab + bc + ca = 71.

▶ Now,

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

= ( 15 ) ( 83 - ( 71 ) ).

= 15 × 12.

= 180.