If $a + b + c = 6$ and $a^2 + b^2 + c^2 = 38$, then what is the value of $a(b^2 + c^2) + b(c^2 + a^2) + c(a^2 + b^2) + 3abc$?
Answer & explanation
Correct answer: option 4
If $a + b + c = 6$
$a^2 + b^2 + c^2 = 38$,
Then what is the value of $a(b^2 + c^2) + b(c^2 + a^2) + c(a^2 + b^2) + 3abc$
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 $a + b = 6$
$a^2 + b^2 = 38$,
( a + b )2 = a2 + b2 + 2ab
( 6 )2 = 38 + 2ab
36 = 38 + 2ab
ab = -1
Then what is the value of $a(b^2) + b(a^2)$ = ab ( a + b)
ab ( a + b) = -1 (6) = -6