Question

Suppose x is a non zero real number such that both x^5 and 20x+19/x are rational number. Prove that x is a rational number

Answer 1

Step-by-step explanation:

Given

x^5 is a rational number

for this the value of x must be a rational number

so let the value of x is 3/2

now the value of

20x + 19/x is

20×3/2 + 19×2/3

30+38/3

128/3

this is also a rational number and if both values are rational when x is rational so the x is a rational number.

Answer 2

Answer:

Official RMO Solution