If $a + b + c = 5$ and $a^3 + b^3 + c^3 - 3abc = 185$, then the value of $ab + bc + ca$ lies between :

-7 and -3

If $a + b + c = 5$

$a^3 + b^3 + c^3 - 3abc = 185$

then the value of $ab + bc + ca$ lies between= ?

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 $a + b = 5$

$a^3 + b^3 = 185$

then the value of $ab$ = ?

We know that,

(a + b)³ = a³ + b³ + 3ab(a+b)

(5)³ = 185 + 3ab(5)

125 - 185 = 15ab

15ab = -60

ab = -4

So, the value of $ab + bc + ca$ lies between -7 and -3