Mister Exam
x²-2xy+y²=4; 4x²+3y=1
The solution
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2 2 x - 2*x*y + y = 4
$$y^{2} + \left(x^{2} - 2 x y\right) = 4$$
2 4*x + 3*y = 1
$$4 x^{2} + 3 y = 1$$
4*x^2 + 3*y = 1
Rapid solution
$$x_{1} = - \frac{7}{4}$$
=
$$- \frac{7}{4}$$
=
$$y_{1} = - \frac{15}{4}$$
=
$$- \frac{15}{4}$$
=
=
$$- \frac{7}{4}$$
=
-1.75
$$y_{1} = - \frac{15}{4}$$
=
$$- \frac{15}{4}$$
=
-3.75
$$x_{2} = 1$$
=
$$1$$
=
$$y_{2} = -1$$
=
$$-1$$
=
=
$$1$$
=
1
$$y_{2} = -1$$
=
$$-1$$
=
-1
$$x_{3} = - \frac{511}{960} - \frac{67 \sqrt{71} i}{960} + \frac{\left(\frac{13}{8} + \frac{\sqrt{71} i}{8}\right)^{2}}{5} + \frac{2 \left(\frac{13}{8} + \frac{\sqrt{71} i}{8}\right)^{3}}{15}$$
=
$$- \frac{3}{8} + \frac{\sqrt{71} i}{8}$$
=
$$y_{3} = \frac{13}{8} + \frac{\sqrt{71} i}{8}$$
=
$$\frac{13}{8} + \frac{\sqrt{71} i}{8}$$
=
=
$$- \frac{3}{8} + \frac{\sqrt{71} i}{8}$$
=
-0.375 + 1.05326872164704*i
$$y_{3} = \frac{13}{8} + \frac{\sqrt{71} i}{8}$$
=
$$\frac{13}{8} + \frac{\sqrt{71} i}{8}$$
=
1.625 + 1.05326872164704*i
$$x_{4} = - \frac{511}{960} + \frac{2 \left(\frac{13}{8} - \frac{\sqrt{71} i}{8}\right)^{3}}{15} + \frac{\left(\frac{13}{8} - \frac{\sqrt{71} i}{8}\right)^{2}}{5} + \frac{67 \sqrt{71} i}{960}$$
=
$$- \frac{3}{8} - \frac{\sqrt{71} i}{8}$$
=
$$y_{4} = \frac{13}{8} - \frac{\sqrt{71} i}{8}$$
=
$$\frac{13}{8} - \frac{\sqrt{71} i}{8}$$
=
=
$$- \frac{3}{8} - \frac{\sqrt{71} i}{8}$$
=
-0.375 - 1.05326872164704*i
$$y_{4} = \frac{13}{8} - \frac{\sqrt{71} i}{8}$$
=
$$\frac{13}{8} - \frac{\sqrt{71} i}{8}$$
=
1.625 - 1.05326872164704*i