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

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

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