The product of two numbers x and y is 45 and their sum is 14. Find the sum of their cubes.

Correct option is C

Given:

The product of the two numbers: xy = 45

The sum of the two numbers: x + y = 14

Concept Used:

​$$x^3 + y^3 = (x + y) \left( (x + y)^2 - 3xy \right)$$​

Solution:

$$x^3 + y^3 = (x + y) \left( (x + y)^2 - 3xy \right)\\ \ \\x^3 + y^3 = 14 \left( 14^2 - 3 \times 45 \right)\\ \ \\x^3 + y^3 = 14 \left( 196 - 135 \right)\\ \ \\x^3 + y^3 = 14 \times 61\\ \ \\x^3 + y^3 = 854$$​