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January 30th, 2019, 07:43 AM   #1
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Find

If x(y+z)=39,
y(z+x)=60,
z(y+x)=63
Find x^2+y^2+z^2
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January 30th, 2019, 09:14 AM   #2
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eq(1)+eq(2)-eq(3) gives xy=12 .
Same thing is for yz and xz .
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January 30th, 2019, 09:15 AM   #3
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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...
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January 30th, 2019, 09:29 AM   #4
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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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