Question

If a + b + C is equal to 9 and a b + BC + CA is equal to 26 find a square + b square + c square

Answer 1

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given that

a + b +  c = 9 .....(1)

ab + bc + ca = 26.....(2)

a² + b² + c² = ?

we know that

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

now let us square equation (1) on both sides

( a + b + c )² = ( 9 )²

a² + b² + c² + 2 ( ab + bc + ca ) = 81

substituting the values of ab  + bc +ca on the above equation

we get

a² + b² + c² + 2(26) = 81

=> a² + b² + c² = 81 / 52

a² + b² + c² = 1.55

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