Question

If a+b+c=8 and a2+b2+c2=16 then find ab+bc+ca

Answer 1

Answer :-

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Given ,

a + b + c = 8

And ,

a² + b² + c² = 16

To find ,

The value of :- ab + bc + ca

Now ,

a² + b² + c² = 16

=> ( a + b + c )² - 2 ( ab + bc + ca ) = 16

[ • Using Identity ]

=> ( 8 )² - 2 ( ab + bc + ca ) = 16

[ • Putting the value of ( a + b + c ) ]

=> 64 - 2 ( ab + bc + ca ) = 16

=> - 2 ( ab + bc + ca ) = 16 - 64

=> - 2 ( ab + bc + ca ) = - 48

=> 2 ( ab + bc + ca ) = 48

=> ( ab + bc + ca ) = 48 / 2

=> ( ab + bc + ca ) = 24 [ ★ Required answer ]

So , the value of ( ab + bc + ca ) is 24.

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