Question

The differences between two numbers is 5 and the product is 14. Find the difference between their cubes.

Answer 1

Let the first number be a
Second number = a - 5
According to question,
a ( a - 5) = 14
=> a^2 - 5a = 14
=> a^2 - 5a - 14 = 0
=> a^2 - 7a + 2a - 14 = 0
=> a(a-7) + 2(a-7) = 0
=> (a-7) (a+2) = 0
a = 7 and - 2
Neglecting negative value, we get

a = 7

First number = 7

Second number = 2

Now,

Difference of their cubes = ( 7)^3 - (2)^3

= 343 - 8

= 335

this is the simple method hope it helps