Question

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

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

Answer 2

$5x^2-6xy+5y^2=29\ 7x^2-8xy+7y^2=43\ \ 5(x^2+y^2)=29+6xy\ 7(x^2+y^2)=43+8xy\ \ frac{7}{5}=frac{43+8xy}{29+6xy}\ 7(29+6xy)=5(43+8xy)\ 203+42xy=215+40xy\ 2xy=12\ xy=6\ y=frac{6}{x}\ 5x^2-36+5*frac{36}{x^2}=29\ 5x^4-36x^2+180=29x^2\ 5x^4-65x^2+180=0\ x=+-2\ x=+-3\ y=+-3\ y=+-2$