document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1202304>Question 1202304</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The sum of the squares of two numbers is 218 and their difference multiplied by the smaller number equals 42. Find the two numbers. </SPAN>\n" );
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document.write( "Answer: The two numbers are 13 and 7\r<BR>\n" );
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document.write( "Work Shown:\r<BR>\n" );
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document.write( "x and y are the two numbers<BR>\n" );
document.write( "Let x > y<BR>\n" );
document.write( "I'll assume both are integers.\r<BR>\n" );
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document.write( "x^2 + y^2 = 218 ... sum of squares<BR>\n" );
document.write( "y^2 = 218 - x^2<BR>\n" );
document.write( "y = sqrt(218 - x^2)\r<BR>\n" );
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document.write( "x-y = difference<BR>\n" );
document.write( "y(x-y) = 42<BR>\n" );
document.write( "xy - y^2 = 42<BR>\n" );
document.write( "x*sqrt(218-x^2) - (218 - x^2) = 42<BR>\n" );
document.write( "x*sqrt(218-x^2) - 218 + x^2 = 42<BR>\n" );
document.write( "x*sqrt(218-x^2) - 218 + x^2 - 42 = 0\r<BR>\n" );
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document.write( "Use a graphing calculator such as Desmos or GeoGebra to plot<BR>\n" );
document.write( "f(x) = x*sqrt(218-x^2) - 218 + x^2 - 42\r<BR>\n" );
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document.write( "You should find one of the x intercepts is x = 13<BR>\n" );
document.write( "y = sqrt(218 - x^2)<BR>\n" );
document.write( "y = sqrt(218 - 13^2)<BR>\n" );
document.write( "y = 7\r<BR>\n" );
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document.write( "The two numbers are 13 and 7.\r<BR>\n" );
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document.write( "Check:<BR>\n" );
document.write( "7^2 + 13^2 = 49 + 169 = 218<BR>\n" );
document.write( "7*(13-7) = 7*6 = 42<BR>\n" );
document.write( "The answers are confirmed.<BR>\n" );
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