document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=922109>Question 922109</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find three numbers in A.P. such that their sum is 27 and the sum of their squares is 341.. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #559380 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=559380\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Find three numbers in A.P. such that their sum is 27 and the sum of their squares is 341..<BR>\n" );
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document.write( "a + (a+d) + (a+2d) = 27<BR>\n" );
document.write( "a^2 + (a+d)^2 + (a+2d)^2 = 341<BR>\n" );
document.write( "-------<BR>\n" );
document.write( "3a + 3d = 27<BR>\n" );
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document.write( "a + d = 9<BR>\n" );
document.write( "a^2 + 9^2 + (9+d)^2 = 341<BR>\n" );
document.write( "------<BR>\n" );
document.write( "a + d = 9<BR>\n" );
document.write( "a^2 + 9^2 + 9^2 + 18d + d^2 = 341<BR>\n" );
document.write( "a^2 +18d + 162 + d^2 = 341<BR>\n" );
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document.write( "a + d = 9<BR>\n" );
document.write( "a^2 + 18d + d^2 = 179<BR>\n" );
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document.write( "a = 9-d<BR>\n" );
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document.write( "(9-d)^2 + 18d + d^2 = 179<BR>\n" );
document.write( "81-18d+d^2 + 18d + d^2 = 179<BR>\n" );
document.write( "81 + 2d^2 = 179<BR>\n" );
document.write( "2d^2 = 98<BR>\n" );
document.write( "d^2 = 49<BR>\n" );
document.write( "d = 7<BR>\n" );
document.write( "Then a = 2<BR>\n" );
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document.write( "Checking::<BR>\n" );
document.write( "Sum = 27 ??<BR>\n" );
document.write( "2 + (2+7) + (2+14) = 6 + 21 = 27<BR>\n" );
document.write( "2^2 + 9^2 + 16^2 = 341<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );