Multiplying (4), (5), and (6) by *x*, *y*, and *z* and adding, we obtain

so,

Hence, from (4), (5), and (6), we have

Putting these values of *x*, *y*, and *z* inn *lx* + *my* + *nz* = 0, we get

Since *λ*_{2} ≠ 0, the equation giving the values of *r*^{2}, the squares of the length of the semi-axes, is

**EXAMPLE 5.110**

If *a*, *b*, and, *c* are positive and

show that a stationary value of *u* is given by

where μ is ...

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