Question

这道数学题怎么化解！求数学高数指导！！！

如图片！怎么由方程组计算得到那个驻点的？！

Answer 1

I change "lambda" to "c" .
I believe that there is conditions: x > 0, y > 0, z > 0.

y+z+ 2cx = 0 (1)
x+z+ 2cy = 0 (2)
y+x +2cz = 0 (3)
x^2 + y^2 + z^2 = 4R^2 (4)

(1)+(2)+(3): 2(x+y+z) + 2c(x+y+z) = 2(1+c)(x+y+z) = 0 (5)
x+y+z > 0 ==> c = -1
By (1), y+z-2x=0, x=y/2+z/2.
By (2), y + y/2 + z/2 - 2z = 0. y=z.
So, x = y = z.
By (4), x^2 = (4/3)R^2
x = y = z = 2R/3^(1/2)

Answer 2

由前3个方程可以看到·xyz是相等的··所以用第4个方程就解出来咯···