document.write( "Question 677089: use a quadratic equation to find two real numbers that satisfy each situation, or show that no such numbers exist
\n" ); document.write( "their sum is 12, and their product is20 \n" ); document.write( "

Algebra.Com's Answer #420675 by stanbon(75887) $\"\"$ $\"About$

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show that no such numbers exist
\n" ); document.write( "their sum is 12, and their product is 20
\n" ); document.write( "-----
\n" ); document.write( "Equations:
\n" ); document.write( "x + y = 12
\n" ); document.write( "xy = 20
\n" ); document.write( "---
\n" ); document.write( "Substitute for \"x\" and try to solve:
\n" ); document.write( "(12-y)y = 20
\n" ); document.write( "----
\n" ); document.write( "12y - y^2 = 20
\n" ); document.write( "----
\n" ); document.write( "y^2 - 12y + 20 = 0
\n" ); document.write( "-----
\n" ); document.write( "y = [12 +- sqrt(144-4*20)]/2
\n" ); document.write( "----
\n" ); document.write( "y = [12 +- sqrt(64)]/2
\n" ); document.write( "---
\n" ); document.write( "y = [12+-8]/2
\n" ); document.write( "y = 10 or y = 2
\n" ); document.write( "---
\n" ); document.write( "If y = 10, x = 2
\n" ); document.write( "If y = 2, y = 2
\n" ); document.write( "====================
\n" ); document.write( "The numbers DO exist.
\n" ); document.write( "====================
\n" ); document.write( "Cheers,
\n" ); document.write( "Stan H. \n" ); document.write( "

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