Question

The sum of the two natural numbers is 30. The difference between the squares of
these two numbers is 240. Find the numbers. Also find the sum of their cubes​

Answer 1

Answer:

19, 11

8190

Step-by-step explanation:

x + y = 30

$x^{2}$ - $y^{2}$ = 240

(x + y)(x - y) = $x^{2}$ - $y^{2}$

therefore, x - y =  $\frac{(x^{2} - y^{2}) }{(x - y)}$  = 240/30 = 8

(1)  .... x + y = 30

(2) .... x - y = 8

(1) + (2)...   2x = 38

therefore, x = 38/2 = 19

x - y = 8

x - 8 = y

therefore, y = 19 - 8 = 11

Therefore, the numbers are 19 and 11

$19^3 = 6859\\11^3 = 1331$

$Therefore, 19^3 + 11^3 = 8190$

Therefore, the sum of the cubes is 8190