Question

5x^2-6xy+5y^2=29
7x^2-8xy+7y^2=43
Решить систему

Answer 1

5(х^2-2ху+у^2)+4ху=29 
7(х^2-2ху+у^2)+6ху=43 

х^2-2ху+у^2=(x-y)^2=a
xy=b
5a+4b=29
7a+6b=43
6b=43-7a
b=(43-7a)/b
a=1
b=6
xy=6
(x-y)^2=1
x=6/y
(6-y^2/y)^2=1
36-12y+y^4-y^2=0
y^4-y^2-12y+36=0