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

 

√x + √y + √z = 10

x + y + z = 42

√(xy) + √(xz) + √(yz) = 29

or, if there is no such triple, enter the word "none" as your answer.

 Jul 29, 2021
 #1
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√x + √y + √z = 10

x + y + z = 42

√(xy) + √(xz) + √(yz) = 29

 

Hello Guest!

 

1 + 4 + 5 = 10

1 + 16 + 25 = 42

√(1*16) + √(1*25) + √(16*25) = 29

x = 1    y = 16    z = 25

laugh  !

 Jul 29, 2021
edited by asinus  Jul 29, 2021
edited by asinus  Jul 29, 2021

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