r+#i*x

50=1/(#i*yc+1/(#i*xl+r+#i*x))

r<50

;Simp(Solve(User,yc))
yc=(x+xl)/(x^2+2*xl*x+r^2+xl^2)

xl=-SQRT(-r)*SQRT(r-50)-x

yc=SQRT(r-50)/(50*SQRT(-r))

50=#i*xl+1/(#i*yc+1/(r+#i*x))

r>50

yc=SQRT(2)*(SQRT(r)*SQRT(x^2+r*(r-50))+5*SQRT(2)*x)/(10*(x^2+r^2))

;Simp(Solve(User,xl))
xl=5*SQRT(2)*SQRT(x^2+r*(r-50))/SQRT(r)

VECTOR(VECTOR([r,x,SQRT(r-50)/(50*SQRT(-r)),-SQRT(-r)*SQRT(r-50)-x],x,-100,10~
0,10),r,10,40,10)

;Simp(User)
[[[10,-100,0.04,120],[10,-90,0.04,110],[10,-80,0.04,100],[10,-70,0.04,90],[10~
,-60,0.04,80],[10,-50,0.04,70],[10,-40,0.04,60],[10,-30,0.04,50],[10,-20,0.04~
,40],[10,-10,0.04,30],[10,0,0.04,20],[10,10,0.04,10],[10,20,0.04,0],[10,30,0.~
04,-10],[10,40,0.04,-20],[10,50,0.04,-30],[10,60,0.04,-40],[10,70,0.04,-50],[~
10,80,0.04,-60],[10,90,0.04,-70],[10,100,0.04,-80]],[[20,-100,0.0244948,124.4~
94],[20,-90,0.0244948,114.494],[20,-80,0.0244948,104.494],[20,-70,0.0244948,9~
4.4948],[20,-60,0.0244948,84.4948],[20,-50,0.0244948,74.4948],[20,-40,0.02449~
48,64.4948],[20,-30,0.0244948,54.4948],[20,-20,0.0244948,44.4948],[20,-10,0.0~
244948,34.4948],[20,0,0.0244948,24.4948],[20,10,0.0244948,14.4948],[20,20,0.0~
244948,4.49489],[20,30,0.0244948,-5.5051],[20,40,0.0244948,-15.5051],[20,50,0~
.0244948,-25.5051],[20,60,0.0244948,-35.5051],[20,70,0.0244948,-45.5051],[20,~
80,0.0244948,-55.5051],[20,90,0.0244948,-65.5051],[20,100,0.0244948,-75.5051]~
],[[30,-100,0.0163299,124.494],[30,-90,0.0163299,114.494],[30,-80,0.0163299,1~
04.494],[30,-70,0.0163299,94.4948],[30,-60,0.0163299,84.4948],[30,-50,0.01632~
99,74.4948],[30,-40,0.0163299,64.4948],[30,-30,0.0163299,54.4948],[30,-20,0.0~
163299,44.4948],[30,-10,0.0163299,34.4948],[30,0,0.0163299,24.4948],[30,10,0.~
0163299,14.4948],[30,20,0.0163299,4.49489],[30,30,0.0163299,-5.5051],[30,40,0~
.0163299,-15.5051],[30,50,0.0163299,-25.5051],[30,60,0.0163299,-35.5051],[30,~
70,0.0163299,-45.5051],[30,80,0.0163299,-55.5051],[30,90,0.0163299,-65.5051],~
[30,100,0.0163299,-75.5051]],[[40,-100,0.01,120],[40,-90,0.01,110],[40,-80,0.~
01,100],[40,-70,0.01,90],[40,-60,0.01,80],[40,-50,0.01,70],[40,-40,0.01,60],[~
40,-30,0.01,50],[40,-20,0.01,40],[40,-10,0.01,30],[40,0,0.01,20],[40,10,0.01,~
10],[40,20,0.01,0],[40,30,0.01,-10],[40,40,0.01,-20],[40,50,0.01,-30],[40,60,~
0.01,-40],[40,70,0.01,-50],[40,80,0.01,-60],[40,90,0.01,-70],[40,100,0.01,-80~
]]]

;Simp(Solve(#5',x))
x=-SQRT(r-50)*SQRT(-r)

-SQRT(r-50)*SQRT(-r)

VECTOR(VECTOR([r,x,SQRT(2)*(SQRT(r)*SQRT(x^2+r*(r-50))+5*SQRT(2)*x)/(10*(x^2+~
r^2)),5*SQRT(2)*SQRT(x^2+r*(r-50))/SQRT(r)],x,-100,100,10),r,10,100,10)

;Simp(User)
[[[10,-100,-0.00556259,219.089],[10,-90,-0.00618989,196.214],[10,-80,-0.00697~
83,173.205],[10,-70,-0.008,150],[10,-60,-0.00937885,126.491],[10,-50,-0.01134~
84,102.469],[10,-40,-0.0144165,77.4596],[10,-30,-0.02,50],[10,-20,-0.04,0],[1~
0,-10,-0.05+0.0387298*#i,38.7298*#i],[10,0,0.0894427*#i,44.7213*#i],[10,10,0.~
05+0.0387298*#i,38.7298*#i],[10,20,0.04,0],[10,30,0.04,50],[10,40,0.0326423,7~
7.4596],[10,50,0.027113,102.469],[10,60,0.0230535,126.491],[10,70,0.02,150],[~
10,80,0.017637,173.205],[10,90,0.0157613,196.214],[10,100,0.0142393,219.089]]~
,[[20,-100,-0.00371934,153.297],[20,-90,-0.00414444,136.93],[20,-80,-0.004681~
41,120.415],[20,-70,-0.00538247,103.682],[20,-60,-0.00633974,86.6025],[20,-50~
,-0.00773513,68.9202],[20,-40,-0.01,50],[20,-30,-0.0146504,27.3861],[20,-20,-~
0.025+0.0111803*#i,22.3606*#i],[20,-10,-0.02+0.0282842*#i,35.3553*#i],[20,0,0~
.0387298*#i,38.7298*#i],[20,10,0.02+0.0282842*#i,35.3553*#i],[20,20,0.025+0.0~
111803*#i,22.3606*#i],[20,30,0.0315034,27.3861],[20,40,0.03,50],[20,50,0.0267~
476,68.9202],[20,60,0.0236602,86.6025],[20,70,0.0210326,103.682],[20,80,0.018~
8479,120.415],[20,90,0.017032,136.93],[20,100,0.0155114,153.297]],[[30,-100,-~
0.00228441,125.166],[30,-90,-0.00254644,111.803],[30,-80,-0.00287787,98.3192]~
,[30,-70,-0.00331143,84.6561],[30,-60,-0.00390524,70.7106],[30,-50,-0.0047753~
2,56.2731],[30,-40,-0.00620204,40.8248],[30,-30,-0.0092131,22.3606],[30,-20,-~
0.0153846+0.0084265*#i,18.2574*#i],[30,-10,-0.01+0.0173205*#i,28.8675*#i],[30~
,0,0.0210818*#i,31.6227*#i],[30,10,0.01+0.0173205*#i,28.8675*#i],[30,20,0.015~
3846+0.0084265*#i,18.2574*#i],[30,30,0.0241202,22.3606],[30,40,0.0257979,40.8~
248],[30,50,0.0246364,56.2731],[30,60,0.0227614,70.7106],[30,70,0.0208265,84.~
6561],[30,80,0.0190399,98.3192],[30,90,0.0174535,111.803],[30,100,0.0160642,1~
25.166]],[[40,-100,-0.00106589,109.544],[40,-90,-0.00118704,98.107],[40,-80,-~
0.00133974,86.6025],[40,-70,-0.00153846,75],[40,-60,-0.00180837,63.2455],[40,~
-50,-0.00219809,51.2347],[40,-40,-0.00281754,38.7298],[40,-30,-0.004,25],[40,~
-20,-0.01,0],[40,-10,-0.00588235+0.0091129*#i,19.3649*#i],[40,0,0.0111803*#i,~
22.3606*#i],[40,10,0.00588235+0.0091129*#i,19.3649*#i],[40,20,0.01,0],[40,30,~
0.02,25],[40,40,0.0221824,38.7298],[40,50,0.0221921,51.2347],[40,60,0.0212685~
,63.2455],[40,70,0.02,75],[40,80,0.0186602,86.6025],[40,90,0.0173696,98.107],~
[40,100,0.0161754,109.544]],[[50,-100,0,100],[50,-90,0,90],[50,-80,0,80],[50,~
-70,0,70],[50,-60,0,60],[50,-50,0,50],[50,-40,0,40],[50,-30,0,30],[50,-20,0,2~
0],[50,-10,0,10],[50,0,0,0],[50,10,0.0076923,10],[50,20,0.0137931,20],[50,30,~
0.017647,30],[50,40,0.0195121,40],[50,50,0.02,50],[50,60,0.0196721,60],[50,70~
,0.0189189,70],[50,80,0.0179775,80],[50,90,0.0169811,90],[50,100,0.016,100]],~
[[60,-100,0.000939924,93.9858],[60,-90,0.00104071,85.1469],[60,-80,0.00116515~
,76.3762],[60,-70,0.00132239,67.7003],[60,-60,0.00152679,59.1607],[60,-50,0.0~
0180193,50.8264],[60,-40,0.00218863,42.8174],[60,-30,0.00276142,35.3553],[60,~
-20,0.00366025,28.8675],[60,-10,0.00513047,24.1522],[60,0,0.00745355,22.3606]~
,[60,10,0.0105358,24.1522],[60,20,0.0136602,28.8675],[60,30,0.0160947,35.3553~
],[60,40,0.0175732,42.8174],[60,50,0.0181953,50.8264],[60,60,0.0181934,59.160~
7],[60,70,0.0177929,67.7003],[60,80,0.0171651,76.3762],[60,90,0.0164253,85.14~
69],[60,100,0.0156458,93.9858]],[[70,-100,0.0017673,90.2377],[70,-90,0.001948~
12,82.3754],[70,-80,0.00216803,74.642],[70,-70,0.00244029,67.082],[70,-60,0.0~
0278423,59.7614],[70,-50,0.00322862,52.7798],[70,-40,0.00381652,46.2909],[70,~
-30,0.00461121,40.5321],[70,-20,0.00569803,35.8568],[70,-10,0.00716515,32.732~
6],[70,0,0.00903507,31.6227],[70,10,0.0111651,32.7326],[70,20,0.0132452,35.85~
68],[70,30,0.014956,40.5321],[70,40,0.0161242,46.2909],[70,50,0.0167421,52.77~
98],[70,60,0.0169018,59.7614],[70,70,0.016726,67.082],[70,80,0.0163273,74.642~
],[70,90,0.0157942,82.3754],[70,100,0.0151901,90.2377]],[[80,-100,0.00249112,~
88.034],[80,-90,0.00273205,81.0092],[80,-80,0.00302024,74.1619],[80,-70,0.003~
36938,67.5462],[80,-60,0.00379795,61.2372],[80,-50,0.00433076,55.3398],[80,-4~
0,0.005,50],[80,-30,0.00584432,45.4147],[80,-20,0.00690188,41.8329],[80,-10,0~
.00819162,39.5284],[80,0,0.00968245,38.7298],[80,10,0.0112685,39.5284],[80,20~
,0.0127842,41.8329],[80,30,0.0140635,45.4147],[80,40,0.015,50],[80,50,0.01556~
67,55.3398],[80,60,0.0157979,61.2372],[80,70,0.0157587,67.5462],[80,80,0.0155~
202,74.1619],[80,90,0.0151458,81.0092],[80,100,0.0146862,88.034]],[[90,-100,0~
.00311938,86.9226],[90,-90,0.0034025,80.6225],[90,-80,0.00373545,74.5355],[90~
,-70,0.00413024,68.7184],[90,-60,0.00460187,63.2455],[90,-50,0.00516844,58.21~
41],[90,-40,0.00585021,53.7483],[90,-30,0.00666666,50],[90,-20,0.00762974,47.~
1404],[90,-10,0.00873278,45.3382],[90,0,0.00993807,44.7213],[90,10,0.0111718,~
45.3382],[90,20,0.0123356,47.1404],[90,30,0.0133333,50],[90,40,0.0140976,53.7~
483],[90,50,0.0146024,58.2141],[90,60,0.0148582,63.2455],[90,70,0.0148994,68.~
7184],[90,80,0.0147699,74.5355],[90,90,0.0145136,80.6225],[90,100,0.0141691,8~
6.9226]],[[100,-100,0.00366025,86.6025],[100,-90,0.00397039,80.932],[100,-80,~
0.00432906,75.4983],[100,-70,0.0047458,70.3562],[100,-60,0.00523152,65.5743],~
[100,-50,0.00579795,61.2372],[100,-40,0.00645614,57.4456],[100,-30,0.00721356~
,54.3139],[100,-20,0.00806952,51.9615],[100,-10,0.00900941,50.4975],[100,0,0.~
01,50],[100,10,0.0109896,50.4975],[100,20,0.0119156,51.9615],[100,30,0.012718~
1,54.3139],[100,40,0.0133526,57.4456],[100,50,0.0137979,61.2372],[100,60,0.01~
4055,65.5743],[100,70,0.0141417,70.3562],[100,80,0.0140851,75.4983],[100,90,0~
.0139151,80.932],[100,100,0.0136602,86.6025]]]