Question

if a^2+b^2+c^2=20 and a+b+c=0; find ab+bc+ac​

Answer 1

Please check the image description

Answer 2

Question:-

If a² + b² + c² = 20 and a + b + c = 0 , find ab + bc + ac

Solution:-

Given :-

=> a² + b² + c² = 20 and

=> a + b + c = 0

To find

=> ab + bc + ac

Using this identities

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

Now put the value on this identities

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

=> ( 0 )² = 20 + 2 ( ab + bc + ac )

=> 0 = 20 + 2 ( ab + bc + ac )

=> -20 = 2 ( ab + bc + ac )

=> ab + bc + ac = - 20 / 2

=> ab + bc + ac= -10

Some more identities

i) ( a + b )² = a² + b² + 2ab

ii) ( a - b )² = a² + b² - 2ab

iii) ( a² - b² ) = ( a - b )(a + b )

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

iv) ( a - b - c )² = a² + b² + c² - 2ab + 2bc - 2ac