Question

a + b + c = 11 ; a^2 + b^2 + c^2 = 81 find: ab + bc + ca

Answer 1

In the above Question , the following information is given -

a + b + c = 11 and a² + b² + c² = 81

To find -

Find the value of ab + bc + ac .

Solution -

Here ,

a + b + c = 11

Squaring both sides ,

( a + b + c )² = ( 11 )²

=> ( a + b + c )² = 121

=> a² + b² + c² + 2 ( ab + bc + ac ) = 121

Now ,

a² + b² + c² = 81 .

So,

=> a² + b² + c² + 2 ( ab + bc + ac ) = 121

=> 81 + 2 ( ab + bc + ac ) = 121

=> 2 ( ab + bc + ac ) = 40

=> ab + bc + ac = 20.

Thus , the required value of ab + bc + ac is 20 .

This is the answer .

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