document.write( "Question 222358: hey there thanks ,the question is-
\n" ); document.write( "the difference between two numbers is 4 and the sum of their squares is80 less than three times their product. Find the numbers
\n" ); document.write( "thanks again.
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Algebra.Com's Answer #166605 by ankor@dixie-net.com(22740)\"\" \"About 
You can put this solution on YOUR website!
the difference between two numbers is 4
\n" ); document.write( "x - y = 4
\n" ); document.write( "or
\n" ); document.write( "x = (y + 4)
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\n" ); document.write( "\"the sum of their squares is 80 less than three times their product.\"
\n" ); document.write( "x^2 + y^2 = 3xy - 80
\n" ); document.write( "x^2 - 3xy + y^2 = -80
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\n" ); document.write( "replace x with (y+4)
\n" ); document.write( "(y+4)^2 - 3y(y+4) + y^2 = -80
\n" ); document.write( "y^2 + 8y + 16 - 3y^2 - 12y + y^2 = -80
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\n" ); document.write( "Combine like terms
\n" ); document.write( "y^2 + y^2 - 3y^2 + 8y - 12y + 16 + 80 = 0
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\n" ); document.write( "-y^2 - 4y + 96 = 0
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\n" ); document.write( "Multiply by -1
\n" ); document.write( "y^2 + 4y - 96 = 0
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\n" ); document.write( "Factor:
\n" ); document.write( "(y+12)(y-8) = 0
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\n" ); document.write( "Positive solution
\n" ); document.write( "y = 8
\n" ); document.write( "find x
\n" ); document.write( "x = 8 + 4
\n" ); document.write( "x = 12
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\n" ); document.write( "Check
\n" ); document.write( "12^2 + 8^2 = 3*12*8 - 80
\n" ); document.write( "144 + 64 = 288 - 80
\n" ); document.write( "208 = 208
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\n" ); document.write( "How about the solution y = -12?
\n" ); document.write( "then
\n" ); document.write( "x = -12 - 4
\n" ); document.write( "x = -16
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\n" ); document.write( "-16^2 + -12^2 = 3*-16*-12 - 80
\n" ); document.write( "256 + 144 = 576 - 80
\n" ); document.write( "not a solution\r
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