Find x, y, and z such that x³+y³+z³=k, for each k from 1 to 100.
Answers
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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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
x³+y³+z³=k,
x = ∛k , y = 0 , z = 0 will satisfy
Learn More:
Simplify (x³-y³)³+(y³-z³)
brainly.in/question/10505873