+647
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
Your last equation should be: sqrtxy + sqrtxz + sqrtyz = 31 NOT 30 !!
By simple iteration x=4, y=9, z=25
+128475 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
