Question

if a + b + C is equal to 9 a square + b square + c square is equal to 250 what is a b + BC + CA​

Answer 1

Answer:

Required value of ab + bc + ca is - 169 / 2.

Step-by-step explanation:

Given,

a + b + c = 9 ... ( 1 )

a^2 + b^2 + c^2 = 250

Squaring on both sides of ( 1 ) :

= > ( a + b + c )^2 = 9^2

= > a^2 + b^2 + c^2 + 2( ab + bc + ca ) = 81 { ( a + b + c )^2 = a^2 + b^2 + c^2 +2( ab + bc + ca ) }

= > 250 + 2( ab + bc + ca ) = 81

= > 2( ab + bc + ca ) = 81 - 250

= > 2( ab + bc + ca ) = - 169

= > ab + bc + ca = - 169 / 2

Hence the required value of ab + bc + ca is - 169 / 2.

Answer 2

Answer:

$\boxed{\boxed{\frac{ - 169}{2}}}$

Step-by-step explanation:

a + b + c = 9 ...........(1)

a + b + c = 9 ...........(1)a² + b² + c² = 250 ...........(2)

We will use identity to solve this problem,

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

Look at the equation marked as (1) and (2) ,and think if the value given to us can be substituted in the above equation.

Yes, we can substitute the values so let's do it,

( 9 )² = 250 + 2 ( ab + bc + ca )

Simplifying the above equation,

81 = 250 + 2 ( ab + bc + ca )

81 - 250 = 2 ( ab + bc + ca )

- 169 = 2 ( ab + bc + ca )

- 169 / 2 = ( ab + bc + ca )

Exchanging LHS & RHS to get the standard form of an equation,

( ab + bc + ca ) = - 169 / 2