Question

If a+b+c=6 and a power2+b power2+ c power2=14 then find ab+bc+ca

Answer 1

Solution:-

Given:-

=> a + b + c = 6

=> a² + b² + c² = 14

To find value of

=> ab + bc + ca

Using this identities

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

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

Now put the value on formula

=> ( 6 )² = 14 + 2( ab + bc + ca )

=> 36 = 14 + 2( ab + bc + ca )

=> 36 - 14 = 2( ab + bc + ca )

=> 22 = 2( ab + bc + ca )

=> ab + bc + ca = 22/2

=> ab + bc + ca = 11

Some more identities

=> (a - b )(a + b ) = a² - b²

=> ( a + b )² = a² + b² + 2ab

=> ( a - b )² = a² + b² - 2ab

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