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# Ordered triple

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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
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#1
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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
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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
edited by CPhill  Jan 25, 2018

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