Question

Answer this Question -

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

Answer 1

Step-by-step explanation:

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

x=∛2 , y = ∛2 , z = 0

x=∛2 , y = 1 , z = 1

This way we can have so many solution

Easiest :

x³+y³+z³=k,

x = ∛k , y = 0 , z = 0 will satisfy

Learn More:

Simplify (x³-y³)³+(y³-z³)

Answer 2

Answer:

I would assume that you want (x,y,z) to be an integer?

then:

k = 1 ----> (1,0,0) or (0,1,0) or (0,0,1)

k = 2 ----> (1,1,0) or

k = 3 ---> (1,1,1)

k = 4 ---- breakdown!

k = 73 ---> (4,1,2) or

if (x,y,z) is from the set of real numbers, you have an infinite number of cases

e.g.

k = 10 ---> (2,1,1), that's nice, or ( 3^(1/3), 1, 6^(1/3) ) or

k = 95 ----> (3,4, 4^(1/3))

Here are the results of the values of k, x, y, z in groups of 4 for the values of k produced by integers x,y, and z from -50 to 50

Step-by-step explanation:

hope this helps