What is the value of $a^2+b^2+c^2$, if a + b + c = 9 and ab + bc + ca = 23 ?

35

If a + b + c = 9

ab + bc + ca = 23

If the number of equation is less then the number of variables then we can put the extra variables according to our choice.

Here the number of variables are 3 and the number of equations are two than put c = 0

a + b = 9

ab = 23

$a^2+b^2+0$ = ?

( a + b )² = a² + b² + 2ab

( 9 )² = a² + b² + 2 × 23

a² + b² = 81 - 46 = 35