Question

Find x, y, and z such that x³+y³+z³=k, for each k from 1 to 100.​

Answer 1

Given : x³+y³+z³=k , k from 1 to 100

To Find : x, y, and z

Solution:

This Question can have lot of solutions as constraints are very less

there is no information whether x , y & z are integer

+ ve , Real numbers

k = 1

x= 1 , y = 0 , z = 0

x =0 , y = 1 , z = 0

x = 0 , y = 0 , = 1

k=2

x= 1 , y = 1 , z = 0

x =0 , y = 1 , z = 1

x = 1 , y = 0 , = 1

k = 3

x= 1 , y = 1 , z = 3

x = 1 , y = 1 , z = 1

x = 1 , y = 0 , = 1

k = 4

x=∛3 , y = 1 , z = 0

This way we can have so many solution

Easiest :

x³+y³+z³=k,

x = ∛k , y = 0 , z = 0 will satisfy

Answer 2

The possible values of k are 1, 2, 3, 8, 9, 10, 17, 24, 43, 62 and 81

The equation is given as:

$x^3 + y^3 + z^3 = k$

To determine the values of k for the equation $x^3 + y^3 + z^3 = k$, we simply set the values of x, y and z to 1,2,3....... while $1 \le k \le 100$ is true.

Some possible scenarios are:

When k = 1, we have the following possible values

• $(x,y,z) = (0,0,1)$
• $(x,y,z) = (0,1,0)$
• $(x,y,z) = (1,0,0)$

When k = 2, we have the following possible values

• $(x,y,z) = (1,1,0)$
• $(x,y,z) = (1,0,1)$
• $(x,y,z) = (0,1,1)$

When k = 3, we have the following possible value

• $(x,y,z) = (1,1,1)$

Hence, the possible values of k are 1, 2, 3, 8, 9, 10, 17, 24, 43, 62 and 81

Read more about equations at:

https://brainly.com/question/2972832