前>>671
>>658
cosθ=(→PA・→PB)/|→PA||→PB|
=(p^4-3p^2+3)/√｛p^8+(10-6p)p^4+5p^4-14p^2+9｝
｛-sinθdθ(p^8-6p^6+15p^4-14p^2+9)^(3/2)｝/dp=(4p^3-6p)(p^8-6p^6+15p^4-14p^2+9)-(p^4-3p^2+3)(8p^7-36p^+60p^3-28p)
=4p^11-30p^9+96p^7-146p^+120p^3-54p
-8p^11+60p^9-192p^7+316p^5-264p^3+84p
=-4p^11+30p^9-96p^7+170p^5-144p^3+30p=0
2p^10-15p^8+48p^6-85p^4+72p^2-15=0
Pのy座標をp^2=Yとすると、
2Y^5-15Y^4+48Y^3-85Y^2+72Y-15=0
(2Y^5-2Y^4-2Y^3)-13Y^4+50Y^3-85Y^2+72Y-15=0
(2Y^5-2Y^4-2Y^3)-13Y^4+13Y^3+37Y^3+13Y^2-98Y^2+72Y-15=0
(2Y^5-2Y^4-2Y^3)-(13Y^4-13Y^3-13Y^2)+37Y^3-98Y^2+72Y-15=0
(2Y^5-2Y^4-2Y^3)-(13Y^4-13Y^3-13Y^2)+(37Y^3-37Y^2-37Y)-61Y^2+109Y-15=0
(2Y^5-2Y^4-2Y^3)-(13Y^4-13Y^3-13Y^2)+(37Y^3-37Y^2-37Y)-61Y^2+61Y+61+48Y-76=0
Y=(1+√5)/2とすると、
24(1+√5)-76=24√5-52＞0
∴Pのy座標は1.618よりやや小さい。