If $a^3 + b^3 + c^3 - 3abc = 250 $ and a + b + c = 10, then what will be the value of $\frac{1}{5} (ab + bc + ca)$ ?

5

If $a^3 + b^3 + c^3 - 3abc = 250 $

a + b + c = 10,

then what will be the value of $\frac{1}{5} (ab + bc + ca)$ = ?

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^3 + b^3= 250 $

a + b = 10,

then what will be the value of $\frac{1}{5} (ab)$ = ?

(a + b)³ = a³ + b³ + 3ab(a+b)

(10)³ = 250 + 3ab(10)

1000 = 250 + 30ab

30ab = 750

ab = 25

and $\frac{1}{5} (ab)$ = $\frac{1}{5} (25)$ = 5