Mister Exam
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How to use it?
- (x+y+2x)(3x-2y); (x+y²+z)(x-z)
- x/3-(y-2x)/5=1/3; y/2+5/6=(x+y)/3
- 5х-7у=9; 6х+5у=-16
-
16x+32y-212,479=0; 32x+128y-791,249=0
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Identical expressions
- (x+y+2x)(3x-2y); (x+y²+z)(x-z)
- (x plus y plus 2x)(3x minus 2y); (x plus y² plus z)(x minus z)
- x+y+2x3x-2y; x+y²+zx-z
-
Similar expressions
- (x+y-2x)(3x-2y); (x+y²+z)(x-z)
- (x-y+2x)(3x-2y); (x+y²+z)(x-z)
- (x+y+2x)(3x+2y); (x+y²+z)(x-z)
- (x+y+2x)(3x-2y); (x+y²-z)(x-z)
- (x+y+2x)(3x-2y); (x-y²+z)(x-z)
- (x+y+2x)(3x-2y); (x+y²+z)(x+z)
(x+y+2x)(3x-2y); (x+y²+z)(x-z)
The solution
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(x + y + 2*x)*(3*x - 2*y) = 0
$$\left(2 x + \left(x + y\right)\right) \left(3 x - 2 y\right) = 0$$
/ 2 \ \x + y + z/*(x - z) = 0
$$\left(x - z\right) \left(z + \left(x + y^{2}\right)\right) = 0$$
(x - z)*(z + x + y^2) = 0
Rapid solution
$$x_{1} = \frac{- 2187 z^{5} + 486 z^{4} + \left(\frac{1}{6} - \frac{\sqrt{1 - 36 z}}{6}\right)^{5} \left(162 z - 36\right) + \left(\frac{1}{6} - \frac{\sqrt{1 - 36 z}}{6}\right)^{4} \left(729 z^{2} - 12\right) + \left(\frac{1}{6} - \frac{\sqrt{1 - 36 z}}{6}\right)^{3} \left(567 z^{2} - 126 z + 8\right) + \left(\frac{1}{6} - \frac{\sqrt{1 - 36 z}}{6}\right)^{2} \left(- 2187 z^{4} + 1215 z^{3} - 162 z^{2}\right) + \left(\frac{1}{6} - \frac{\sqrt{1 - 36 z}}{6}\right) \left(405 z^{3} - 54 z^{2}\right)}{27 z^{2} \left(9 z - 1\right) \left(9 z + 2\right)}$$
=
$$\frac{\sqrt{1 - 36 z}}{18} - \frac{1}{18}$$
=
$$y_{1} = \frac{1}{6} - \frac{\sqrt{1 - 36 z}}{6}$$
=
$$\frac{1}{6} - \frac{\sqrt{1 - 36 z}}{6}$$
=
=
$$\frac{\sqrt{1 - 36 z}}{18} - \frac{1}{18}$$
=
0.037037037037037*(486*z^4 - 2187*z^5 + (0.166666666666667 - 1*(0.0277777777777778 - z)^0.5)^2*(1215*z^3 - 162*z^2 - 2187*z^4) + (0.166666666666667 - 1*(0.0277777777777778 - z)^0.5)^3*(8 + 567*z^2 - 126*z) + (0.166666666666667 - 1*(0.0277777777777778 - z)^0.5)^4*(-12 + 729*z^2) + (0.166666666666667 - 1*(0.0277777777777778 - z)^0.5)^5*(-36 + 162*z) + (0.166666666666667 - 1*(0.0277777777777778 - z)^0.5)*(405*z^3 - 54*z^2))/(z^2*(2 + 9*z)*(-1 + 9*z))
$$y_{1} = \frac{1}{6} - \frac{\sqrt{1 - 36 z}}{6}$$
=
$$\frac{1}{6} - \frac{\sqrt{1 - 36 z}}{6}$$
=
0.166666666666667 - 1*(0.0277777777777778 - z)^0.5
$$x_{2} = \frac{- 2187 z^{5} + 486 z^{4} + \left(162 z - 36\right) \left(\frac{\sqrt{1 - 36 z}}{6} + \frac{1}{6}\right)^{5} + \left(729 z^{2} - 12\right) \left(\frac{\sqrt{1 - 36 z}}{6} + \frac{1}{6}\right)^{4} + \left(405 z^{3} - 54 z^{2}\right) \left(\frac{\sqrt{1 - 36 z}}{6} + \frac{1}{6}\right) + \left(\frac{\sqrt{1 - 36 z}}{6} + \frac{1}{6}\right)^{3} \left(567 z^{2} - 126 z + 8\right) + \left(\frac{\sqrt{1 - 36 z}}{6} + \frac{1}{6}\right)^{2} \left(- 2187 z^{4} + 1215 z^{3} - 162 z^{2}\right)}{27 z^{2} \left(9 z - 1\right) \left(9 z + 2\right)}$$
=
$$- \frac{\sqrt{1 - 36 z}}{18} - \frac{1}{18}$$
=
$$y_{2} = \frac{\sqrt{1 - 36 z}}{6} + \frac{1}{6}$$
=
$$\frac{\sqrt{1 - 36 z}}{6} + \frac{1}{6}$$
=
=
$$- \frac{\sqrt{1 - 36 z}}{18} - \frac{1}{18}$$
=
0.037037037037037*(486*z^4 - 2187*z^5 + (0.166666666666667 + 1*(0.0277777777777778 - z)^0.5)^2*(1215*z^3 - 162*z^2 - 2187*z^4) + (0.166666666666667 + 1*(0.0277777777777778 - z)^0.5)^3*(8 + 567*z^2 - 126*z) + (0.166666666666667 + 1*(0.0277777777777778 - z)^0.5)^4*(-12 + 729*z^2) + (0.166666666666667 + 1*(0.0277777777777778 - z)^0.5)^5*(-36 + 162*z) + (0.166666666666667 + 1*(0.0277777777777778 - z)^0.5)*(405*z^3 - 54*z^2))/(z^2*(2 + 9*z)*(-1 + 9*z))
$$y_{2} = \frac{\sqrt{1 - 36 z}}{6} + \frac{1}{6}$$
=
$$\frac{\sqrt{1 - 36 z}}{6} + \frac{1}{6}$$
=
0.166666666666667 + 1*(0.0277777777777778 - z)^0.5
$$x_{3} = \frac{- 2187 z^{5} + 486 z^{4} + \left(162 z - 36\right) \left(- \frac{\sqrt{1 - 9 z}}{3} - \frac{1}{3}\right)^{5} + \left(729 z^{2} - 12\right) \left(- \frac{\sqrt{1 - 9 z}}{3} - \frac{1}{3}\right)^{4} + \left(405 z^{3} - 54 z^{2}\right) \left(- \frac{\sqrt{1 - 9 z}}{3} - \frac{1}{3}\right) + \left(- \frac{\sqrt{1 - 9 z}}{3} - \frac{1}{3}\right)^{3} \left(567 z^{2} - 126 z + 8\right) + \left(- \frac{\sqrt{1 - 9 z}}{3} - \frac{1}{3}\right)^{2} \left(- 2187 z^{4} + 1215 z^{3} - 162 z^{2}\right)}{27 z^{2} \left(9 z - 1\right) \left(9 z + 2\right)}$$
=
$$- \frac{2 \sqrt{1 - 9 z}}{9} - \frac{2}{9}$$
=
$$y_{3} = - \frac{\sqrt{1 - 9 z}}{3} - \frac{1}{3}$$
=
$$- \frac{\sqrt{1 - 9 z}}{3} - \frac{1}{3}$$
=
=
$$- \frac{2 \sqrt{1 - 9 z}}{9} - \frac{2}{9}$$
=
0.037037037037037*(486*z^4 - 2187*z^5 + (-0.333333333333333 - 1*(0.111111111111111 - z)^0.5)^2*(1215*z^3 - 162*z^2 - 2187*z^4) + (-0.333333333333333 - 1*(0.111111111111111 - z)^0.5)^3*(8 + 567*z^2 - 126*z) + (-0.333333333333333 - 1*(0.111111111111111 - z)^0.5)^4*(-12 + 729*z^2) + (-0.333333333333333 - 1*(0.111111111111111 - z)^0.5)^5*(-36 + 162*z) + (-0.333333333333333 - 1*(0.111111111111111 - z)^0.5)*(405*z^3 - 54*z^2))/(z^2*(2 + 9*z)*(-1 + 9*z))
$$y_{3} = - \frac{\sqrt{1 - 9 z}}{3} - \frac{1}{3}$$
=
$$- \frac{\sqrt{1 - 9 z}}{3} - \frac{1}{3}$$
=
-0.333333333333333 - 1*(0.111111111111111 - z)^0.5
$$x_{4} = \frac{- 2187 z^{5} + 486 z^{4} + \left(162 z - 36\right) \left(\frac{\sqrt{1 - 9 z}}{3} - \frac{1}{3}\right)^{5} + \left(729 z^{2} - 12\right) \left(\frac{\sqrt{1 - 9 z}}{3} - \frac{1}{3}\right)^{4} + \left(405 z^{3} - 54 z^{2}\right) \left(\frac{\sqrt{1 - 9 z}}{3} - \frac{1}{3}\right) + \left(\frac{\sqrt{1 - 9 z}}{3} - \frac{1}{3}\right)^{3} \left(567 z^{2} - 126 z + 8\right) + \left(\frac{\sqrt{1 - 9 z}}{3} - \frac{1}{3}\right)^{2} \left(- 2187 z^{4} + 1215 z^{3} - 162 z^{2}\right)}{27 z^{2} \left(9 z - 1\right) \left(9 z + 2\right)}$$
=
$$\frac{2 \sqrt{1 - 9 z}}{9} - \frac{2}{9}$$
=
$$y_{4} = \frac{\sqrt{1 - 9 z}}{3} - \frac{1}{3}$$
=
$$\frac{\sqrt{1 - 9 z}}{3} - \frac{1}{3}$$
=
=
$$\frac{2 \sqrt{1 - 9 z}}{9} - \frac{2}{9}$$
=
0.037037037037037*(486*z^4 - 2187*z^5 + (-0.333333333333333 + 1*(0.111111111111111 - z)^0.5)^2*(1215*z^3 - 162*z^2 - 2187*z^4) + (-0.333333333333333 + 1*(0.111111111111111 - z)^0.5)^3*(8 + 567*z^2 - 126*z) + (-0.333333333333333 + 1*(0.111111111111111 - z)^0.5)^4*(-12 + 729*z^2) + (-0.333333333333333 + 1*(0.111111111111111 - z)^0.5)^5*(-36 + 162*z) + (-0.333333333333333 + 1*(0.111111111111111 - z)^0.5)*(405*z^3 - 54*z^2))/(z^2*(2 + 9*z)*(-1 + 9*z))
$$y_{4} = \frac{\sqrt{1 - 9 z}}{3} - \frac{1}{3}$$
=
$$\frac{\sqrt{1 - 9 z}}{3} - \frac{1}{3}$$
=
-0.333333333333333 + 1*(0.111111111111111 - z)^0.5
$$x_{5} = \frac{- 243 z^{5} \left(162 z - 36\right) - 2187 z^{5} + 81 z^{4} \left(729 z^{2} - 12\right) + 486 z^{4} - 27 z^{3} \left(567 z^{2} - 126 z + 8\right) + 9 z^{2} \left(- 2187 z^{4} + 1215 z^{3} - 162 z^{2}\right) - 3 z \left(405 z^{3} - 54 z^{2}\right)}{27 z^{2} \left(9 z - 1\right) \left(9 z + 2\right)}$$
=
$$z$$
=
$$y_{5} = - 3 z$$
=
$$- 3 z$$
=
=
$$z$$
=
0.037037037037037*(486*z^4 - 2187*z^5 + 9*z^2*(1215*z^3 - 162*z^2 - 2187*z^4) + 81*z^4*(-12 + 729*z^2) - 3*z*(405*z^3 - 54*z^2) - 27*z^3*(8 + 567*z^2 - 126*z) - 243*z^5*(-36 + 162*z))/(z^2*(2 + 9*z)*(-1 + 9*z))
$$y_{5} = - 3 z$$
=
$$- 3 z$$
=
-3*z
$$x_{6} = \frac{\frac{243 z^{5} \left(162 z - 36\right)}{32} - 2187 z^{5} + \frac{81 z^{4} \left(729 z^{2} - 12\right)}{16} + 486 z^{4} + \frac{27 z^{3} \left(567 z^{2} - 126 z + 8\right)}{8} + \frac{9 z^{2} \left(- 2187 z^{4} + 1215 z^{3} - 162 z^{2}\right)}{4} + \frac{3 z \left(405 z^{3} - 54 z^{2}\right)}{2}}{27 z^{2} \left(9 z - 1\right) \left(9 z + 2\right)}$$
=
$$z$$
=
$$y_{6} = \frac{3 z}{2}$$
=
$$\frac{3 z}{2}$$
=
=
$$z$$
=
0.037037037037037*(486*z^4 - 2187*z^5 + 1.5*z*(405*z^3 - 54*z^2) + 2.25*z^2*(1215*z^3 - 162*z^2 - 2187*z^4) + 3.375*z^3*(8 + 567*z^2 - 126*z) + 5.0625*z^4*(-12 + 729*z^2) + 7.59375*z^5*(-36 + 162*z))/(z^2*(2 + 9*z)*(-1 + 9*z))
$$y_{6} = \frac{3 z}{2}$$
=
$$\frac{3 z}{2}$$
=
1.5*z