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 January 30th, 2019, 07:43 AM #1 Member   Joined: Oct 2012 Posts: 73 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: iPhone Posts: 480 Thanks: 73 eq(1)+eq(2)-eq(3) gives xy=12 . Same thing is for yz and xz . Thanks from fahad nasir and topsquark
 January 30th, 2019, 09:15 AM #3 Math Team   Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,316 Thanks: 1023 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... Thanks from fahad nasir, topsquark and JeffM1
 January 30th, 2019, 09:29 AM #4 Global Moderator   Joined: Dec 2006 Posts: 20,472 Thanks: 2039 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. Thanks from fahad nasir, topsquark and JeffM1

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