The number 1729 is the smallest number that can be expressed as the sum of two cubes in two different ways as 1729 = 12^3 + 1^3 = 10^3 + 9^3. Find two other numbers with the same property. Express them as the sum of two cubes.

4104 and 13832

Step-by-step explanation:

This type of number is known as the Hardy-Ramanujan Number.

We have that 1729 is the first number where this is found, but there are others. The second number that meets this is:

4104

2 ^ 3 + 16 ^ 3 = 9 ^ 3 + 15 ^ 3

And we also have:

13832

18 ^ 3 + 20 ^ 3 = 2 ^ 3 + 24 ^ 3

That is to say, the numbers 4104 and 13832 comply with this property

the direct variation says that:

then the equation is of the form is given by:

            where k is the constant variation.

from the given table:

consider any value of x and m(x)=y

x = 2 and m(x)=y = 3

substitute these value in [1]; we have;

divide both sides by 2 we get;

⇒

check:

put x = -1 and m(x) = -1.5

substitute in the equation:

-1.5 = -1.5                   true

therefore, the function m(x) represents a direct variation

graph of this function as shown below:

24 units

step-by-step explanation: