1樓：匿名使用者
不知你的什麼版本，我是2011a就告訴我no explicit solution即無解析解。沒有出現你這種情況。
這個方程組就是求兩圓交點，頂多有兩組解，你仔細看解出來的x第一個和x第二個是一模一樣的。後兩個也是一樣的。我以前用低版本的matlab(7.
0.1)，似乎得到過你這樣的解，但是現在用新版本的做就沒有這樣的問題。
no explicit solution的話，需要求數值解了（matlab說沒解析解，不等於你就算不出來了，它經常會告訴你沒解析解的，不要吃驚）。其實你這裡手算很好算的，何必讓電腦去幫你做。matlab符號解方程的能力非常有限，只能夠解很簡單的有解析解的方程，它的優勢在於數值運算，就是你給出除了x,y以外其他變數的數值然後讓它解。
2樓：書宬
>> syms x y xp yp xi yi min
f1=(x-xp)^2+(y-yp)^2-min^2;
f2=(x-xi)^2+(y-yi)^2-3*min^2;
d=solve(f1,f2,x,y)
d =x: [2x1 sym]
y: [2x1 sym]
>> d.x
ans =
1/2*(-(2*min^2*yp-yp^2*yi+xi^2*yi-2*xi*xp*yp-2*xi*xp*yi+yp^3+xp^2*yi-yp*yi^2+xp^2*yp-2*min^2*yi+yp*xi^2+yi^3+(48*xi^2*xp^2*min^2+4*xp^4*yi*yp+4*xp^2*yi^3*yp+2*xi*xp*yi^4+8*xi*xp^3*yi^2+8*xi*xp^3*yp^2+2*xi*xp*yp^4-12*xi^2*xp^2*yp^2+4*xi^4*yi*yp+8*xi^2*yi^2*min^2+4*xi^2*yi^3*yp-12*xi^2*yi^2*xp^2+8*xi^3*yi^2*xp+4*yp^3*yi*xi^2+4*yp^3*yi*xp^2-6*yp^2*yi^2*xp^2-6*yp^2*yi^2*xi^2+8*min^2*yp^2*xi^2+8*min^2*yp^2*xp^2+8*xi*xp*min^4-32*xi^3*xp*min^2-32*xi*xp^3*min^2+8*xp^2*yi^2*min^2+12*yp^2*yi^2*xi*xp-8*yp^3*yi*xi*xp-16*min^2*yp*xp^2*yi-16*min^2*yp^2*xi*xp-16*min^2*yp*xi^2*yi-16*xi*xp^3*yp*yi-yp^4*xi^2-2*xp^4*yi^2-xp^2*yi^4+24*xi^2*yi*xp^2*yp-16*xi^3*yi*xp*yp-xp^6-xi^6-2*xi^4*yi^2-xi^2*yi^4-8*xi*xp*yp*yi^3-yp^4*xp^2-16*xi*xp*yi^2*min^2+8*xi^3*xp*yp^2+32*min^2*yp*xi*xp*yi+6*xi^5*xp-4*xi^2*min^4+8*xi^4*min^2-4*xp^2*min^4+8*xp^4*min^2+6*xi*xp^5+20*xi^3*xp^3-15*xi^2*xp^4-15*xi^4*xp^2-2*xp^4*yp^2-2*yp^2*xi^4)^(1/2))/(-2*xi*xp-2*yp*yi+yp^2+yi^2+xp^2+xi^2)*yp+(2*min^2*yp-yp^2*yi+xi^2*yi-2*xi*xp*yp-2*xi*xp*yi+yp^3+xp^2*yi-yp*yi^2+xp^2*yp-2*min^2*yi+yp*xi^2+yi^3+(48*xi^2*xp^2*min^2+4*xp^4*yi*yp+4*xp^2*yi^3*yp+2*xi*xp*yi^4+8*xi*xp^3*yi^2+8*xi*xp^3*yp^2+2*xi*xp*yp^4-12*xi^2*xp^2*yp^2+4*xi^4*yi*yp+8*xi^2*yi^2*min^2+4*xi^2*yi^3*yp-12*xi^2*yi^2*xp^2+8*xi^3*yi^2*xp+4*yp^3*yi*xi^2+4*yp^3*yi*xp^2-6*yp^2*yi^2*xp^2-6*yp^2*yi^2*xi^2+8*min^2*yp^2*xi^2+8*min^2*yp^2*xp^2+8*xi*xp*min^4-32*xi^3*xp*min^2-32*xi*xp^3*min^2+8*xp^2*yi^2*min^2+12*yp^2*yi^2*xi*xp-8*yp^3*yi*xi*xp-16*min^2*yp*xp^2*yi-16*min^2*yp^2*xi*xp-16*min^2*yp*xi^2*yi-16*xi*xp^3*yp*yi-yp^4*xi^2-2*xp^4*yi^2-xp^2*yi^4+24*xi^2*yi*xp^2*yp-16*xi^3*yi*xp*yp-xp^6-xi^6-2*xi^4*yi^2-xi^2*yi^4-8*xi*xp*yp*yi^3-yp^4*xp^2-16*xi*xp*yi^2*min^2+8*xi^3*xp*yp^2+32*min^2*yp*xi*xp*yi+6*xi^5*xp-4*xi^2*min^4+8*xi^4*min^2-4*xp^2*min^4+8*xp^4*min^2+6*xi*xp^5+20*xi^3*xp^3-15*xi^2*xp^4-15*xi^4*xp^2-2*xp^4*yp^2-2*yp^2*xi^4)^(1/2))/(-2*xi*xp-2*yp*yi+yp^2+yi^2+xp^2+xi^2)*yi+xp^2+yp^2+2*min^2-xi^2-yi^2)/(xp-xi)
1/2*(-(2*min^2*yp-yp^2*yi+xi^2*yi-2*xi*xp*yp-2*xi*xp*yi+yp^3+xp^2*yi-yp*yi^2+xp^2*yp-2*min^2*yi+yp*xi^2+yi^3-(48*xi^2*xp^2*min^2+4*xp^4*yi*yp+4*xp^2*yi^3*yp+2*xi*xp*yi^4+8*xi*xp^3*yi^2+8*xi*xp^3*yp^2+2*xi*xp*yp^4-12*xi^2*xp^2*yp^2+4*xi^4*yi*yp+8*xi^2*yi^2*min^2+4*xi^2*yi^3*yp-12*xi^2*yi^2*xp^2+8*xi^3*yi^2*xp+4*yp^3*yi*xi^2+4*yp^3*yi*xp^2-6*yp^2*yi^2*xp^2-6*yp^2*yi^2*xi^2+8*min^2*yp^2*xi^2+8*min^2*yp^2*xp^2+8*xi*xp*min^4-32*xi^3*xp*min^2-32*xi*xp^3*min^2+8*xp^2*yi^2*min^2+12*yp^2*yi^2*xi*xp-8*yp^3*yi*xi*xp-16*min^2*yp*xp^2*yi-16*min^2*yp^2*xi*xp-16*min^2*yp*xi^2*yi-16*xi*xp^3*yp*yi-yp^4*xi^2-2*xp^4*yi^2-xp^2*yi^4+24*xi^2*yi*xp^2*yp-16*xi^3*yi*xp*yp-xp^6-xi^6-2*xi^4*yi^2-xi^2*yi^4-8*xi*xp*yp*yi^3-yp^4*xp^2-16*xi*xp*yi^2*min^2+8*xi^3*xp*yp^2+32*min^2*yp*xi*xp*yi+6*xi^5*xp-4*xi^2*min^4+8*xi^4*min^2-4*xp^2*min^4+8*xp^4*min^2+6*xi*xp^5+20*xi^3*xp^3-15*xi^2*xp^4-15*xi^4*xp^2-2*xp^4*yp^2-2*yp^2*xi^4)^(1/2))/(-2*xi*xp-2*yp*yi+yp^2+yi^2+xp^2+xi^2)*yp+(2*min^2*yp-yp^2*yi+xi^2*yi-2*xi*xp*yp-2*xi*xp*yi+yp^3+xp^2*yi-yp*yi^2+xp^2*yp-2*min^2*yi+yp*xi^2+yi^3-(48*xi^2*xp^2*min^2+4*xp^4*yi*yp+4*xp^2*yi^3*yp+2*xi*xp*yi^4+8*xi*xp^3*yi^2+8*xi*xp^3*yp^2+2*xi*xp*yp^4-12*xi^2*xp^2*yp^2+4*xi^4*yi*yp+8*xi^2*yi^2*min^2+4*xi^2*yi^3*yp-12*xi^2*yi^2*xp^2+8*xi^3*yi^2*xp+4*yp^3*yi*xi^2+4*yp^3*yi*xp^2-6*yp^2*yi^2*xp^2-6*yp^2*yi^2*xi^2+8*min^2*yp^2*xi^2+8*min^2*yp^2*xp^2+8*xi*xp*min^4-32*xi^3*xp*min^2-32*xi*xp^3*min^2+8*xp^2*yi^2*min^2+12*yp^2*yi^2*xi*xp-8*yp^3*yi*xi*xp-16*min^2*yp*xp^2*yi-16*min^2*yp^2*xi*xp-16*min^2*yp*xi^2*yi-16*xi*xp^3*yp*yi-yp^4*xi^2-2*xp^4*yi^2-xp^2*yi^4+24*xi^2*yi*xp^2*yp-16*xi^3*yi*xp*yp-xp^6-xi^6-2*xi^4*yi^2-xi^2*yi^4-8*xi*xp*yp*yi^3-yp^4*xp^2-16*xi*xp*yi^2*min^2+8*xi^3*xp*yp^2+32*min^2*yp*xi*xp*yi+6*xi^5*xp-4*xi^2*min^4+8*xi^4*min^2-4*xp^2*min^4+8*xp^4*min^2+6*xi*xp^5+20*xi^3*xp^3-15*xi^2*xp^4-15*xi^4*xp^2-2*xp^4*yp^2-2*yp^2*xi^4)^(1/2))/(-2*xi*xp-2*yp*yi+yp^2+yi^2+xp^2+xi^2)*yi+xp^2+yp^2+2*min^2-xi^2-yi^2)/(xp-xi)
>> d.y
ans =
1/2*(2*min^2*yp-yp^2*yi+xi^2*yi-2*xi*xp*yp-2*xi*xp*yi+yp^3+xp^2*yi-yp*yi^2+xp^2*yp-2*min^2*yi+yp*xi^2+yi^3+(48*xi^2*xp^2*min^2+4*xp^4*yi*yp+4*xp^2*yi^3*yp+2*xi*xp*yi^4+8*xi*xp^3*yi^2+8*xi*xp^3*yp^2+2*xi*xp*yp^4-12*xi^2*xp^2*yp^2+4*xi^4*yi*yp+8*xi^2*yi^2*min^2+4*xi^2*yi^3*yp-12*xi^2*yi^2*xp^2+8*xi^3*yi^2*xp+4*yp^3*yi*xi^2+4*yp^3*yi*xp^2-6*yp^2*yi^2*xp^2-6*yp^2*yi^2*xi^2+8*min^2*yp^2*xi^2+8*min^2*yp^2*xp^2+8*xi*xp*min^4-32*xi^3*xp*min^2-32*xi*xp^3*min^2+8*xp^2*yi^2*min^2+12*yp^2*yi^2*xi*xp-8*yp^3*yi*xi*xp-16*min^2*yp*xp^2*yi-16*min^2*yp^2*xi*xp-16*min^2*yp*xi^2*yi-16*xi*xp^3*yp*yi-yp^4*xi^2-2*xp^4*yi^2-xp^2*yi^4+24*xi^2*yi*xp^2*yp-16*xi^3*yi*xp*yp-xp^6-xi^6-2*xi^4*yi^2-xi^2*yi^4-8*xi*xp*yp*yi^3-yp^4*xp^2-16*xi*xp*yi^2*min^2+8*xi^3*xp*yp^2+32*min^2*yp*xi*xp*yi+6*xi^5*xp-4*xi^2*min^4+8*xi^4*min^2-4*xp^2*min^4+8*xp^4*min^2+6*xi*xp^5+20*xi^3*xp^3-15*xi^2*xp^4-15*xi^4*xp^2-2*xp^4*yp^2-2*yp^2*xi^4)^(1/2))/(-2*xi*xp-2*yp*yi+yp^2+yi^2+xp^2+xi^2)
1/2*(2*min^2*yp-yp^2*yi+xi^2*yi-2*xi*xp*yp-2*xi*xp*yi+yp^3+xp^2*yi-yp*yi^2+xp^2*yp-2*min^2*yi+yp*xi^2+yi^3-(48*xi^2*xp^2*min^2+4*xp^4*yi*yp+4*xp^2*yi^3*yp+2*xi*xp*yi^4+8*xi*xp^3*yi^2+8*xi*xp^3*yp^2+2*xi*xp*yp^4-12*xi^2*xp^2*yp^2+4*xi^4*yi*yp+8*xi^2*yi^2*min^2+4*xi^2*yi^3*yp-12*xi^2*yi^2*xp^2+8*xi^3*yi^2*xp+4*yp^3*yi*xi^2+4*yp^3*yi*xp^2-6*yp^2*yi^2*xp^2-6*yp^2*yi^2*xi^2+8*min^2*yp^2*xi^2+8*min^2*yp^2*xp^2+8*xi*xp*min^4-32*xi^3*xp*min^2-32*xi*xp^3*min^2+8*xp^2*yi^2*min^2+12*yp^2*yi^2*xi*xp-8*yp^3*yi*xi*xp-16*min^2*yp*xp^2*yi-16*min^2*yp^2*xi*xp-16*min^2*yp*xi^2*yi-16*xi*xp^3*yp*yi-yp^4*xi^2-2*xp^4*yi^2-xp^2*yi^4+24*xi^2*yi*xp^2*yp-16*xi^3*yi*xp*yp-xp^6-xi^6-2*xi^4*yi^2-xi^2*yi^4-8*xi*xp*yp*yi^3-yp^4*xp^2-16*xi*xp*yi^2*min^2+8*xi^3*xp*yp^2+32*min^2*yp*xi*xp*yi+6*xi^5*xp-4*xi^2*min^4+8*xi^4*min^2-4*xp^2*min^4+8*xp^4*min^2+6*xi*xp^5+20*xi^3*xp^3-15*xi^2*xp^4-15*xi^4*xp^2-2*xp^4*yp^2-2*yp^2*xi^4)^(1/2))/(-2*xi*xp-2*yp*yi+yp^2+yi^2+xp^2+xi^2)
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