Find an ordered triple (x,y,z) of real numbers satisfying x <= y <= z and the system of equations

sqrtx + sqrty + sqrtz = 10

x + y + z = 38

sqrtxy + sqrtxz + sqrtyz = 30

waffles
Jan 25, 2018

#1**+1 **

Your last equation should be: sqrtxy + sqrtxz + sqrtyz = 31 NOT 30 !!

By simple iteration x=4, y=9, z=25

Guest Jan 25, 2018

edited by
Guest
Jan 25, 2018

#2**+1 **

If this is

sqrt(x) + sqrt(y) + sqrt(z) = 10

x + y + z = 38

sqrt (xy ) + sqrt (xz ) + sqrt (yz) = 30

No solutions exist

I let a = sqrt (x), b = sqrt(y) and c = sqrt (z)

And...as the guest points out .... there is a solution if the last equation = 31

a = 2 b = 3 and c = 5

So x = 4, y = 9 and z = 25

I can give you the details of my method...if you want them

CPhill
Jan 25, 2018