Question

Sa se determine x e lui Z astfel incat: (x^-x+2)/(x^-1) sa apartina lui z (x^= x patrat)

Answer 1

Explicație pas cu pas:

(x²-x+2)/(x²-1) €Z <=>x²-1|x²-x+2

x²-1|x²-x+2

x²-1|x²-1

=> x²-1|x²-x+2-x²+1 =>x²-1|3-x

x²-1|3-x/*x =>x²-1|3x-x²

x²-1|x²-1

=> x²-1|3x-x²+x²-1 => x²-1|3x-1

x²-1|3x-1

x²-1|3-x/*3=>x²-1|9-3x

=>x²-1|3x-1+9-3x=>x²-1|8=>x²-1€D8 in Z =>

x²-1€{-8,-4,-2,-1,1,2,4,8} =>

x²€{-7,-3,-1,0,2,3,5,9}

Cum x€Z => x²€{0,9}=>

x€{0,3,-3} => S€{0,3} (nu luam -3 deoarece fractia nu mai €Z)