If a + b + c = 6 and $ a^2 + b^2 + c^2 = 40 , $ then what is the value of $a^3 + b^3 + c^3 -3abc ?$
Answer & explanation
Correct answer: option 2
a3 + b3 = ( a + b ) ( a2 + b2 - ab )
( a + b )2 = a2 + b2 + 2ab
If a + b + c = 6
$ a^2 + b^2 + c^2 = 40 , $
what is the value of $a^3 + b^3 + c^3 -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 = 40 , $
( 6 )2 = 40 + 2ab
36 - 40 = 2ab
ab = -2
what is the value of $a^3 + b^3 $ = ( a + b ) ( a2 + b2 - ab )
= $a^3 + b^3 $ = ( 6 ) ( 40 - (-2) )
$a^3 + b^3 $ = 252