Вопрос пользователя:
сколько решений имеет система уравнений x^2+y^2=9 3-xy=0
Илюха отвечает:
right left { {{x^2+y^2=9} atop {-xy=-3}}.right.left { {{x^2+y^2=9} atop {y=3/x}}.right. x^2+(3/x)^2=9.x^2+9/x^2= 9 | *x^2.x^4 + 9 = 9x^2.x^4 -9x^2+ 9 = 0.x^2=a.a^2 -9a+9=0.D=81-36=45.a1=(9+sqrt{45})/2 = (9+ 6.7) / 2 = 7.85.a2 = (9-sqrt{45})/2 = (9- 6.7) / 2= 1.15.x^2 = 7.85 xapprox2.8 xapprox-2.8x^2 = 1.15.xapprox1.07 xapprox-1.07 ” title=”left { {{x^2+y^2=9} atop {3-xy=0}}.right left { {{x^2+y^2=9} atop {-xy=-3}}.right.left { {{x^2+y^2=9} atop {y=3/x}}.right. x^2+(3/x)^2=9.x^2+9/x^2= 9 | *x^2.x^4 + 9 = 9x^2.x^4 -9x^2+ 9 = 0.x^2=a.a^2 -9a+9=0.D=81-36=45.a1=(9+sqrt{45})/2 = (9+ 6.7) / 2 = 7.85.a2 = (9-sqrt{45})/2 = (9- 6.7) / 2= 1.15.x^2 = 7.85 xapprox2.8 xapprox-2.8x^2 = 1.15.xapprox1.07 xapprox-1.07 ” alt=”left { {{x^2+y^2=9} atop {3-xy=0}}.right left { {{x^2+y^2=9} atop {-xy=-3}}.right.left { {{x^2+y^2=9} atop {y=3/x}}.right. x^2+(3/x)^2=9.x^2+9/x^2= 9 | *x^2.x^4 + 9 = 9x^2.x^4 -9x^2+ 9 = 0.x^2=a.a^2 -9a+9=0.D=81-36=45.a1=(9+sqrt{45})/2 = (9+ 6.7) / 2 = 7.85.a2 = (9-sqrt{45})/2 = (9- 6.7) / 2= 1.15.x^2 = 7.85 xapprox2.8 xapprox-2.8x^2 = 1.15.xapprox1.07 xapprox-1.07 ” />.Ответ: система имеет 4 решения.