Is z = <msqrt> <msqrt> 3 x + 1 </msqrt>

Matthew Hubbard

Matthew Hubbard

Answered question

2022-05-13

Is z = 3 x + 1 3 x 1 a rational or irrational number?

Answer & Explanation

cartonarepcpo4

cartonarepcpo4

Beginner2022-05-14Added 12 answers

By sqaring twice we get:
z 4 = 3 x + 1 3 x 1
To get a rational solution we are looking for two squared squares with a difference of two:
3 x + 1 = K 4 3 x 1 = L 4
With L = K 1 we get the smallest distance possible:
K 4 ( K 1 ) 4 = 2
This equation has no integer solution for K. Therefore, no rational value for z can exist.

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