幫幫忙搵個value of v

vcos 40*( (-vsin40-√(〖0.413v〗^2-88.2) )/(-9.8))=60

v(-vsin40-√(〖0.413v〗^2-88.2) = 60(-9.8)/cos40

-(v^2)sin40 - v√(〖0.413v〗^2-88.2) = -588/cos40

[ -v√(〖0.413v〗^2-88.2) ]^2 = [(v^2)sin40 - 588/cos40]^2

(v^2)(〖0.413v〗^2-88.2) = (v^4)(sin40)^2 - 1176(v^2)tan40 + (588/cos40)^2

(v^4)(0.413)^2 - 88.2v^2 = (v^4)(sin40)^2 - 1176(v^2)tan40 + (588/cos40)^2


0 = [(sin40)^2 - 0.413^2]v^4 + (88.2 -1176tan40)v^2 + (588/cos40)^2

0 = 0.242606911 v^4 - 898.5811662 v^2 + 589178.2675

用二次方程求根公式 :

v^2 =

898.5811662(+ -)√[898.5811662^2 - 4(0.242606911)(589178.2675)]
-----------------------------------------------------------------------------------------
----------------------------2(0.242606911)


v^2 = 2852.481891 或 851.3745318

v = (+ - ) 53.40863124 或 (+ - ) 29.17832298

代入原方程檢驗後, v = - 53.40863124 或 29.17832298