Non Linear Equations without the Matrix

[lksgman]

Hello to anyone, first of all I am new in this forum and I recently got my HP Prime. I am using it to study functions with many variables. Right now I am with the topic of Max and Minimum values with restrictions. So after making the derivatives. I get stuck because I do not know how to find the values that will make those values 0 . So please anybody knows how to use the calculator in those aspects.

Example:
F(x,y,z,λ)= xyz-λ(2x+3y+4z-90)

Derivatives
Fx=yz-2λ=0
Fy=xz-3λ=0
Fz=xy-4λ=0
Fλ=-2x-3y-4z-90=0

So I need to find the Xs,Ys,Zs and λs that make those values 0. So that would be it and any help I will appreciate it.

[Han]

In CAS view:

purge(x,y,z,l);
f:=x*y*z-l*(2*x+3*y+4*z-90)
fx:=diff(f,x);
fy:=diff(f,y);
fz:=diff(f,z);
fl:=diff(f,l);
solve({fx=0,fy=0,fz=0,fl=0},{x,y,z,l});

[lksgman]

Thank you so much for the quick response.
Greetings from El Salvador and I appreciate this forum exist.

[roadrunner]

Han,

What am I doing wrong? When I solve this problem in Xcas I get:

[[0,30,0,0],[45,0,0,0],[0,0,45/2,0],[15,10,15/2,75/2]]

When I solve this problem on the prime (CAS approx) I get:

{[(-y+10)/(2*z-15),(-2*z^2-6*l+45*z)/(2*l*z-15*l),(-y*z+2*l)/(2*l*z-15*l),(-3*y^2-16*l+90*y)/(2*l*z-15*l)],[(-y+10)/(2*z-15),(-2*z^2-6*l+45*z)/(2*l*z-15*l),(-y*z+2*l)/(2*l*z-15*l),(-3*y^2-16*l+90*y)/(2*l*z-15*l)]}

On the Prime (CAS exact) I get empty brackets [].

It's the same on the simulator and handheld.

       

-road

[parisse]

This is probably because something has been fixed in Xcas since the last firmware was released.

[roadrunner]

Thank you parisse. I for one am looking forward to that enigmatic future firmware release.

-road