If ( a + b + c) = 7 and ab + bc + ca = 12, find the value of $a^2 +b^2 +c^2$.

25

If ( a + b + c) = 7

ab + bc + ca = 12

find the value of $a^2 +b^2 +c^2$

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 ( a + b) = 7

ab  = 12

find the value of $a^2 +b^2 $ = ?

( a + b )² = a² + b² + 2ab

( 7)² = a² + b² + 2(12)

49 = a² + b² + 24

a² + b² = 25