What is the possible value of ( a + b + c) - 3, if $a^2 + b^2 + c^2= 9$ and ab + bc + ca = 8 ?

2

If $a^2 + b^2 + c^2= 9$ and ab + bc + ca = 8

If the number of variables is more than the number of equations then we can put extra variables according to our choice.

Here the number of variables are 3 and the number of equations are 2 so, we can put c = 0. we get,

$a^2 + b^2 = 9$

ab = 8

( a + b )² = a² + b² + 2ab

( a + b )² = 9+ 2 × 8 = 25

a + b = 5

Put the values in ( a + b + c) - 3

( 5 + 0) - 3 = 2