document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1209508>Question 1209508</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve for x and y;<BR>\n" );
document.write( "√(x)^√(y) + √(y)^√(x) = 145 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #849025 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(53763)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><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/cgi-bin/show-face.mpl?user=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=849025\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .\r<BR>\n" );
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document.write( "As Edwin explained in his post, this equation has infinitely many solutions in real numbers,<BR>\n" );
document.write( "therefore the problem's request, as it is given in the post, makes no sense.\r<BR>\n" );
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document.write( "The problem gets sense, if to ask about solutions in integer positive numbers.\r<BR>\n" );
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document.write( "Notice that \r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;145 = 81 + 64 = 64 + 81,  \r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;or\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;145 = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%5E4 ALIGN=MIDDLE  ALT=\"3%5E4\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%5E3 ALIGN=MIDDLE  ALT=\"4%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%5E3 ALIGN=MIDDLE  ALT=\"4%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%5E4 ALIGN=MIDDLE  ALT=\"3%5E4\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "It gives two solutions in integer positive numbers\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;(a) &nbsp;&nbsp;x = 9, y = 16;\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;(b)  &nbsp;&nbsp;x = 16, y = 9.\r<BR>\n" );
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document.write( "There are other solutions.  Consider this decomposition\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;145 = 144 + 1 = 1 + 144.\r<BR>\n" );
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document.write( "It gives two more solutions in integer numbers\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;(c) &nbsp;&nbsp;x = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12%5E2 ALIGN=MIDDLE  ALT=\"12%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, y = 1;\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;(d)  &nbsp;&nbsp;x = 1, y = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12%5E2 ALIGN=MIDDLE  ALT=\"12%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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