Question

Rezolvat ecuatia x la puterea 4 +4y la puterea 2=2017 in multumea numerelor intregi
Dau corana si 35 puncte

Answer 1

x^4+4y²=2017

4y² par, 2017 impar⇒x^4impar⇒ximpar

x=1, 4y²=2016, y²=504,y∉Q⇒y∉Z

x=3,, x^4=81, 4y²=1936, y²=484, y=+-√484 =+/- 22 este solutie

dar desigur si x=-3 va da x^4=81

x=5, x^4=625, 4y²=1392, y²=348, y∉Q⇒y∉Z

x=7, x^4=2401, 4y²<0, y∉R⇒y∉Z

solutii

x=3; y=22

x=-3;y=22

x=3; y=-22

x=-3; y=-22

4 solutii