问一道解方程组的题☆请写出球方程组的具体步骤用拉格朗日乘子法.令F（x,y,z,λ,μ）=x^2+y^2+z^2+λ(x^2+y^2-z)-μ(x+y+z-1)对每一个自变量求偏导后得方程组F'x=2x+2λx+μ=0①F'y=2y+2λy+μ=0②F'z=2z-λ+μ=0

Question

问一道解方程组的题
☆请写出球方程组的具体步骤
用拉格朗日乘子法.令 F（x,y,z,λ,μ）=x^2+y^2+z^2+λ(x^2+y^2-z)-μ(x+y+z-1)
对每一个自变量求偏导后得方程组
F'x=2x+2λx+μ=0 ①
F'y=2y+2λy+μ=0 ②
F'z=2z-λ+μ=0 ③
F'λ=x^2+y^2-z=0 ④
F'μ=x+y+z-1=0 ⑤
如何求得x=y=（-1±根号3）/2,z=2减加根号3?
打错了：请写出求方程组的具体步骤

Answer 1

2x+2λx+μ=0.① 2y+2λy+μ=0.② 2z-λ+μ=0.③ x^2+y^2-z=0.④ x+y+z-1=0.⑤ ① - ②得:2(x-y) = -2λ(x-y) ,得 x=y .(6)回代入④⑤得:2x^2-z=02x+z-1=0.(7)上述两式相加消去z得:2x^2+2x-1=0 ,得x=(-1±根号3)/2回...