Question

Помогите решить систему уравнений,пожайлуста

Answer 1

2х^8=х⁴у⁴+1
-
3у^8=х⁴у⁴+2
2х^8-3у^8=-1
2х^8=(3у^8)-1
х^8=(3у^8-1)/2
3у^8-1=а;3у^8=1+а;у^8=(1+а)/3;у⁴=√(1+а)/3
х^8=а/2
х⁴=√(а/2)


а=√(а/2)√(1+а)/3+1
а-1=√(а/2)(а+1)/3
а²-2а+1=(а²+а)/6
6а²-12а+6-а²-а=0
5а²-13а+6=0
Д=169-120=49
а=(13±7)/10
а1=2;а2=8/10=4/5

1)х^8=1;х=1
у^8=1+а=3
у=3^(1/8)

2)x^8=a/2=1/2*4/5=4/10=2/5
x=(2/5)^1/8
y^8=a+1=4/5+1=9/5
y=(9/5)^1/8

Answer 2

$\left \{ {{2x^{8}=x^{4}y^{4}+1|3} \atop {3x^{8}=x^{4}y^{4}+2}|-2} \right.\\\\\left \{ {{6x^{y}=3x^{4}y^{4}+3} \atop {-6x^{8}=-2x^{4}y^{4}-4}} \right.\\\\x^{4}y^{4}-1=0\\\\x^{4}y^{4}=1\\\\xy=1\\\\2x^{8}=1+1\\\\2x^{8} =2\\\\x^{8}=1\\\\x_{1}=1,x_{2} =-1\\\\y_{1}=1,y_{2} =-1$

Ответ : (1 ; 1) , (- 1; - 1)