Question

The difference between two positive natural numbers is 2. If the difference between their cubes is 56; find the numbers.​

Answer 1

Answer:

the correct option is A

Explanation:

Let the two numbers be a and b

a−b=2 or a=b+2

a

3

−b

3

=56

(b+2)

3

−b

3

=56

b

3

+8+6b

2

+12b−b

3

=56

6b

2

+12b−48=0

b

2

+2b−8=0

b

2

+4b−2b−8=0

⇒b=−4,2

Hence, a=b+2=4

Thus the numbers are 2 and 4.

Answer 2

Given difference 2 number is 2 and difference between their cubes is 56

Explanation:

• let us assume the 2 positive natural number is a and b
• a-b=2 and
• $a^{3} -b^{3} =56$
• we know that
• $(a-b)^{3}= a^{3} -b^{3} -3ab(a-b)$ and subsituting the known values
• [tex]2^{3} =56-3ab(2)\\ 8=56-6ab\\ 6ab=56-8=48\\ ab=48/6=8\\ ab=8\\ (b+2)b=8\\ b^{2}=2b-8=0\\ (b-4)(b+2)=0[/tex]
• therefore b=4 or -2 since it is a positive number b is 4 and a is 2
• a=2 and b=4