Mister Exam
(3x-2y)(4y-x)=0; x^2-3xy+2y^2=6
The solution
You have entered
[src]
(3*x - 2*y)*(4*y - x) = 0
$$\left(- x + 4 y\right) \left(3 x - 2 y\right) = 0$$
2 2 x - 3*x*y + 2*y = 6
$$2 y^{2} + \left(x^{2} - 3 x y\right) = 6$$
2*y^2 + x^2 - 3*x*y = 6
Rapid solution
$$x_{1} = -4$$
=
$$-4$$
=
$$y_{1} = -1$$
=
$$-1$$
=
=
$$-4$$
=
-4
$$y_{1} = -1$$
=
$$-1$$
=
-1
$$x_{2} = 4$$
=
$$4$$
=
$$y_{2} = 1$$
=
$$1$$
=
=
$$4$$
=
4
$$y_{2} = 1$$
=
$$1$$
=
1
$$x_{3} = \frac{2 \sqrt{6} \left(-4 - \frac{3 \sqrt{6}}{2}\right) \left(4 - \frac{3 \sqrt{6}}{2}\right)}{5}$$
=
$$- \sqrt{6}$$
=
$$y_{3} = - \frac{3 \sqrt{6}}{2}$$
=
$$- \frac{3 \sqrt{6}}{2}$$
=
=
$$- \sqrt{6}$$
=
-2.44948974278318
$$y_{3} = - \frac{3 \sqrt{6}}{2}$$
=
$$- \frac{3 \sqrt{6}}{2}$$
=
-3.67423461417477
$$x_{4} = - \frac{2 \sqrt{6} \left(-4 + \frac{3 \sqrt{6}}{2}\right) \left(\frac{3 \sqrt{6}}{2} + 4\right)}{5}$$
=
$$\sqrt{6}$$
=
$$y_{4} = \frac{3 \sqrt{6}}{2}$$
=
$$\frac{3 \sqrt{6}}{2}$$
=
=
$$\sqrt{6}$$
=
2.44948974278318
$$y_{4} = \frac{3 \sqrt{6}}{2}$$
=
$$\frac{3 \sqrt{6}}{2}$$
=
3.67423461417477
Numerical answer
[src]
x1 = 2.449489742783178 y1 = 3.674234614174767
x2 = -2.449489742783178 y2 = -3.674234614174767
x3 = -4.0 y3 = -1.0
x3 = -4.0 y3 = -1.0