# Given the system #{(x+y+z=a),(x^2+y^2+z^2=b^2),(xy=z^2):}# determine the conditions over #a,b# such that #x,y,z# are distinct positive numbers?

##### 2 Answers

#### Explanation:

In the first octant (

triangular area, with vertices (a, 0, 0), (0, a, 0) and (0, 0, a). The

section of this area by the sphere

only if the length of the perpendicular from the origin on this plane

Consider the third as

hyperbolic cylinder. The part of this in

beyond the plane

For the hyperboloid to meet the section of the other two,

the length of the perpendicular from the origin O on this plane ( that

touches the hyperboloid ).,

Instead, for (c-absent)

Under this condition,

Despite that

surfaces, it is relevant that the section of

z=c is the RH

See below.

#### Explanation:

Substituting

so

but

Solving the polynomial

we have

Attached a figure showing the surfaces,