y2, y3, z = var('y2 y3 z')
energyEquation = y2 + 10000^2/(2*32.2*(40*y2)^2) + z == 200
momentumEquation = 40*y2^2/2 + 10000^2/(32.2*40*y2) == 40*y3^2/2+10000^2/(32.2*40*y3)
knownY3 = y3 == 100 - z
pretty_print( energyEquation )
pretty_print( momentumEquation )
pretty_print( knownY3 )
solution = solve( [ energyEquation, momentumEquation, knownY3 ], y2,y3,z )
pretty_print(Matrix( solution ))
\newcommand{\Bold}[1]{\mathbf{#1}}y_{2} + z + 970.496894409938 \, \frac{1}{y_{2}^{2}} = 200
\newcommand{\Bold}[1]{\mathbf{#1}}20 \, y_{2}^{2} + 77639.7515527950 \, \frac{1}{y_{2}} = 20 \, y_{3}^{2} + 77639.7515527950 \, \frac{1}{y_{3}}
\newcommand{\Bold}[1]{\mathbf{#1}}y_{3} = -z + 100
\newcommand{\Bold}[1]{\mathbf{#1}}\left(y2=49.0151187905y2=2.69155446756y2=(−2.96556297758−0.497581433136i)y2=(−2.96556297758+0.497581433136i)y2=3.9364461738y2=100.288y2=322255322y2=−322255322y3=(−50.5809248555)y3=36.6554809843y3=(−1.51297187707−35.528534053i)y3=(−1.51297187707+35.528534053i)y3=(−33.4331140351)y3=0.384498149358y3=3222525723y3=−3222525723z=150.580912863z=63.3445121951z=(101.512971877+35.528534053i)z=(101.512971877−35.528534053i)z=133.433121019z=99.615503876z=32225(42723−5)2723z=32225(42723+5)2723\right)