求方程x²﹙x²-1﹚=y²﹙y²-1﹚的图像
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![求方程x²﹙x²-1﹚=y²﹙y²-1﹚的图像](/uploads/image/z/3761332-52-2.jpg?t=%E6%B1%82%E6%96%B9%E7%A8%8Bx%26%23178%3B%EF%B9%99x%26%23178%3B%EF%BC%8D1%EF%B9%9A%3Dy%26%23178%3B%EF%B9%99y%26%23178%3B%EF%BC%8D1%EF%B9%9A%E7%9A%84%E5%9B%BE%E5%83%8F)
求方程x²﹙x²-1﹚=y²﹙y²-1﹚的图像
求方程x²﹙x²-1﹚=y²﹙y²-1﹚的图像
求方程x²﹙x²-1﹚=y²﹙y²-1﹚的图像
∵x^2(x^2-1)=y^2(y^2-1),
∴x^4-x^2+1/4=y^4-y^2+1/4,
∴(x^2-1/2)^2=(y^2-1/2)^2,
∴x^2-1/2=y^2-1/2,或x^2-1/2=1/2-y^2.
由x^2-1/2=y^2-1/2,得:y^2=x^2,∴y=x,或y=-x.
由x^2-1/2=1/2-y^2,得:x^2+y^2=1.
∴原方程的图象是过原点且平分坐标轴夹角的两条直线和以原点为圆心、半径为1的圆.