A system within a system

Algebra Level 4

1 x y + 2 y z + 3 x z = 29 72 4 x y + 5 y z + 6 x z = 17 18 7 x y − 8 y z + 9 x z = 43 72 \large \frac{1}{xy} + \frac{2}{yz} + \frac {3}{xz} = \frac {29}{72} \\ \large \frac{4}{xy} + \frac{5}{yz} + \frac {6}{xz} = \frac {17}{18} \\ \large \frac{7}{xy} - \frac{8}{yz} + \frac {9}{xz} = \frac {43}{72}

Given the system of equations above.

Find

( x + y + z ) 2 . \large (x+y+z)^{2}.


The answer is 169.

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Efren Medallo by Efren Medallo , 26, Philippines

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2 solutions

Kevin Tran
Nov 18, 2016

1 Helpful 0 Interesting 0 Brilliant 0 Confused
Jawahar Vasanth
May 3, 2015

Taking 1/x y=a, 1/y z =b , 1/z*x=c, solving these equations

a+2b+3c=29/72 ; 4a +5b +6c=17/18 ; 7a-8b + 9c=43/72 we get a=24 b=18 c=12 (xyz)^2=24 12 18 xyz =72 x=6 y=4 z=3 so (x+y+z)^2=13^2=169

0 Helpful 0 Interesting 0 Brilliant 0 Confused

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