If a + b + c = 10 and ab+ bc+ ca = 30, then the value of $a^2 + b^2 + c^2 $ is :

40

If a + b + c = 10

ab+ bc+ ca = 30,

then 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 = 10

ab = 30,

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

( a + b )² = a² + b² + 2ab

( 10 )² = a² + b² + 2(30)

100 = a² + b² + 60

a² + b² = 100 - 60 = 40