If 9a + 9b +9c = 81 and 4ab + 4bc + 4ca = 160, then what is the value of $6a^2 +6b^2 +6c^2 $ ?

6

If 9a + 9b +9c = 81

4ab + 4bc + 4ca = 160

what is the value of $6a^2 +6b^2 +6c^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 9a + 9b  = 81

then, a + b = 9

4ab  = 160

ab = 40

what is the value of $6a^2 +6b^2 $ ? =  $6(a^2 + b^2) $ ? 

( a + b )² = a² + b² + 2ab

( 9 )² = a² + b² + 2 × 40

81 = a² + b² + 80

a² + b² = 1

And, $6(a^2 + b^2) $  = 6(1) = 6