Question

a+b+c=11,a^2+b^2+c^2=51 what is value of ab+bc+ca

Answer 1

Hey there!!

In order to solve this problem we will use the formula :

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

Let us take a + b + c = 11

Now, let us square this on both sides,

( a + b + c )² = ( 11 ) ²

Use the formula :

a² + b² + c² + 2 ( ab + bc + ca ) = 121

Note : a² + b² + c² = 51

Substitute it

51 + 2 ( ab + bc + ca ) = 121

2 ( ab + bc + ca ) = 121 - 51

2 ( ab + bc + ca ) = 70

ab + bc + ca = 70 ÷ 2

ab + bc + ca = 35

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