If the sum of three numbers is 18 and the sum of their squares is 36, then find the difference between the sum of their cubes and three times of their product.
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. −1944.
Let the three numbers be x, y, and z.
x + y + z = 18
x2 + y2 + z2 = 36
x3 + y3 + z3 - 3xyz = (x + y + z)[3(x2 + y2 + z2) - (x + y + z)2]
⇒ x3 + y3 + z3 - 3xyz = × (18) × [3 × (36) - (18)2]
⇒ x3 + y3 + z3 - 3xyz = 9 × (108 - 324)
⇒ x3 + y3 + z3 - 3xyz = -1944