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受欢迎的代数 >

x/y-y/x = 5/6 ,x^2-y^2=5

解答

\frac{x}{y} - \frac{y}{x} = \frac{5}{6}, x^{2} - y^{2} = 5

解答

x = 3, x = - 3, x = 2 i, x = - 2 i, y = 2 y = - 2 y = - 3 i y = 3 i

求解步骤

[\frac{x}{y} - \frac{y}{x} = \frac{5}{6} x^{2} - y^{2} = 5]

对于

\frac{x}{y} - \frac{y}{x} = \frac{5}{6}

将

x

移到一边:

x = \frac{3 y}{2}, x = - \frac{2 y}{3}

将解

x = \frac{3 y}{2}, x = - \frac{2 y}{3}

代入

x^{2} - y^{2} = 5

对于

x^{2} - y^{2} = 5

，用

\frac{3 y}{2}

替代

x : y = 2, y = - 2

对于

x^{2} - y^{2} = 5

，用

- \frac{2 y}{3}

替代

x : y = - 3 i, y = 3 i

将解

y = 2, y = - 2, y = - 3 i, y = 3 i

代入

\frac{x}{y} - \frac{y}{x} = \frac{5}{6}

对于

\frac{x}{y} - \frac{y}{x} = \frac{5}{6}

，用

2

替代

y : x = 3, x = - \frac{4}{3}

对于

\frac{x}{y} - \frac{y}{x} = \frac{5}{6}

，用

- 2

替代

y : x = - 3, x = \frac{4}{3}

对于

\frac{x}{y} - \frac{y}{x} = \frac{5}{6}

，用

- 3 i

替代

y : x = - \frac{9}{2} i, x = 2 i

对于

\frac{x}{y} - \frac{y}{x} = \frac{5}{6}

，用

3 i

替代

y : x = - 2 i, x = \frac{9}{2} i

将解代入原方程进行验证

因而，

\frac{x}{y} - \frac{y}{x} = \frac{5}{6}, x^{2} - y^{2} = 5

最后的解是

x = 3, x = - 3, x = 2 i, x = - 2 i, y = 2 y = - 2 y = - 3 i y = 3 i

作图

流行的例子

f(x)=x^2-2x+3,f(x)=-2x+19

f (x) = x^{2} - 2 x + 3, f (x) = - 2 x + 19

((x+y))/((x-y))+((x-y))/((x+y))= 13/6 ,xy=5

\frac{( x + y )}{( x - y )} + \frac{( x - y )}{( x + y )} = \frac{13}{6}, x y = 5

x^2+y^2=2,5yx+y-1=0

x^{2} + y^{2} = 2, 5 y x + y - 1 = 0

x+y=2,x(x-y)=12

x + y = 2, x (x - y) = 12

x^2+y^2=2,6y=3-2x

x^{2} + y^{2} = 2, 6 y = 3 - 2 x