document.write( "Question 286767: If x^2 + y^2 = 40 and xy = 12, then x + y =\r
\n" ); document.write( "\n" ); document.write( "A. 7. B. 8. C. 7 or −7. D. 8 or −8. E. None of these. \n" ); document.write( "
Algebra.Com's Answer #207969 by checkley77(12844)\"\" \"About 
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x^2 + y^2 = 40
\n" ); document.write( "xy = 12 or x=12/y
\n" ); document.write( "Now replace x in the first equation with 12/y & solve for y.
\n" ); document.write( "(12/y)^2+y^2=40
\n" ); document.write( "144/y^2+y^2=40
\n" ); document.write( "(144+y^2*y^2)/y^2=40
\n" ); document.write( "144+y^4=40y^2
\n" ); document.write( "y^4-40y^2+144=0
\n" ); document.write( "(y^2-36)(y^2-4)=0
\n" ); document.write( "(y+6)(y-6)(y+2)(y-2)=0
\n" ); document.write( "y+6=0
\n" ); document.write( "y=-6 ans.
\n" ); document.write( "y-6=0
\n" ); document.write( "y=6 ans.
\n" ); document.write( "y+2=0
\n" ); document.write( "y=-2 ans.
\n" ); document.write( "y-2=0
\n" ); document.write( "y=2 ans.
\n" ); document.write( "x=12/+-6=+-2 ans.
\n" ); document.write( "x=12/+-2=+-6 ans.
\n" ); document.write( "Proof:
\n" ); document.write( "262+6^2=40
\n" ); document.write( "4+36=40
\n" ); document.write( "then x + y =2+6=8 ans.
\n" ); document.write( "x+y=-2-6=-8 ans.\r
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