Question

the difference between two numbers is 5 and their 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

Answer 2

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