If a² + b² + c² = 300 and ab + bc + ca = 50, then what is the value of a + b + c ? (Given that a, b and c are all positive.)

20

If a² + b² + c² = 300

ab + bc + ca = 50

Then what is the value of a + b + c = ?

If the number of equations are less than the number of variables then we can put the extra variables according to our choice = 

So here two equations given and three variables are present so put c = 0

If a² + b² = 300

ab  = 50

Then what is the value of a + b = ?

( a + b )² = a² + b² + 2ab

( a + b )² = 300 + 2(50)

( a + b )² = 400

a + b = \(\sqrt {400}\) = 20