Question

how to 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

Learn More:

Simplify (x³-y³)³+(y³-z³)

if x+y+z=0 then the square of the value of

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Answer 2

Answer:

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=³2, y = √2, z = 0

x=√2, y = 1, z = 1