Question

there are two whole numbers, difference of their squares is a cube and the difference of their cubes is a square. These are the smallest possible numbers. Can you find the numbers ?​

Answer 1

The smallest whole number pair such that the difference of their squares is a cube and the difference of their cubes is a square is 1 and 0.

Difference of squares = 1^2 - 0^2 =1 =1^3

Difference of cubes = 1^3 - 0^3 = 1 = 1^2

Hope this helps! :-)

Answer 2

Answer:

0 and 1 are the required two numbers.

Step-by-step explanation:

Given:-

There are two smallest possible whole numbers such that the difference of their square is a cube.

And the difference of their cubes is $a$ square.

To find:-

The required two numbers.

According to the question,

The smallest two possible whole numbers are 0 and 1.

Since the difference of their square is a cube, i.e.,

The difference of $1^2$ and $0^2$ is a cube.

⇒ $1^2-0^2$

⇒ 1 - 0

⇒ 1

⇒ $1^3$

Also it is given that,

The difference of their cubes is a square, i.e.,

The difference of $1^3$ and $0^3$ is a square.

⇒ $1^3-0^3$

⇒ 1 - 0

⇒ 1

⇒ $1^2$

Therefore, 0 and 1 are the required two numbers.

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