January 30th, 2019, 07:43 AM  #1 
Member Joined: Oct 2012 Posts: 78 Thanks: 0  Find
If x(y+z)=39, y(z+x)=60, z(y+x)=63 Find x^2+y^2+z^2 
January 30th, 2019, 09:14 AM  #2 
Senior Member Joined: Dec 2015 From: somewhere Posts: 551 Thanks: 83 
eq(1)+eq(2)eq(3) gives xy=12 . Same thing is for yz and xz . 
January 30th, 2019, 09:15 AM  #3 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,597 Thanks: 1038 
xy + xz + 00 = 39 xy + 00 + yz = 60 00 + xz + yz = 63 3 equations, 3 unknowns...so solve for each unknown. Suggest you use elimination process... 
January 30th, 2019, 09:29 AM  #4 
Global Moderator Joined: Dec 2006 Posts: 20,835 Thanks: 2162 
The given equations are linear in xy, xz and yz, with solution (xy, xz, yz) = (18, 21, 9). Hence x² = (xy)(xz)/(yz) = 9, and, similarly, y² = 36 and z² = 49, so x² + y² + z² = 94. 

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