Question

the difference between two positive integers is 2 and the difference between their cubes is 56 find the numbers

Answer 1

two and four

2 cube = 8

4 cube = 64

4-2=2

and 64-8=56

Answer 2

Answer:

The two numbers are 2 , 4

Step-by-step explanation:

Given,

Difference between two integers is 2

Let one integer be x

So, The other integer will be x + 2

According to question,

The difference between their cubes is 56 , that is,

( x + 2 )³ - x³ = 56

we know,

( a + b )³ = a³ + b³ + 3a²b + 3ab²

Applying this,

x³ + 8 + 6x² +12x - x³ = 56

6x² +12x + 8 = 56

6x² +12x + 8 - 56 = 0

6x² +12x - 48 = 0

Dividing entire equation by 6,

x² + 2x - 8 = 0

x² + 4x - 2x - 8 = 0

x ( x + 4 ) - 2 ( x + 4 ) = 0

( x - 2 ) ( x + 4 ) = 0

x = 2 or x = -4

It is given in question that there are positive integers

So,

x = 2

Second number = x + 2 = 2 + 2 = 4

Hence,

The two numbers are 2 , 4