the difference between two positive integer is 2 and the difference between their cubes is 56 find the numbers
Answers
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
Answer:
Step-by-step explanation: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