document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1150463>Question 1150463</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If x∈Z, what is the sum of the digits of the value x such that √x+⁴√x=30? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #771833 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13219)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=771833\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E%281%2F2%29%2Bx%5E%281%2F4%29+=+30 ALIGN=MIDDLE  ALT=\"x%5E%281%2F2%29%2Bx%5E%281%2F4%29+=+30\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Introduce a new variable to make it easier to see how to solve the problem.<br><BR>\n" );
document.write( "Let y = x^(1/4)<BR>\n" );
document.write( "Then y^2 = x^(1/2)<br><BR>\n" );
document.write( "Then the equation is<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E2%2By+=+30 ALIGN=MIDDLE  ALT=\"y%5E2%2By+=+30\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E2%2By-30+=+0 ALIGN=MIDDLE  ALT=\"y%5E2%2By-30+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%2B6%29%28y-5%29+=+0%0D%0A%7B%7B%7By+=+-6 ALIGN=MIDDLE  ALT=\"y%2B6%29%28y-5%29+=+0%0D%0A%7B%7B%7By+=+-6\"   DISABLED_style= \"max-width:90%; height:auto;\" > or y = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+5 ALIGN=MIDDLE  ALT=\"y+=+5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "y = -6 gives us x^(1/4) = -6, which is not possible.<br><BR>\n" );
document.write( "y = 5 gives us x^(1/4) = 5, which makes x = 5^4 = 625.<br><BR>\n" );
document.write( "ANSWER: The problem asks for the sum of the digits of x, which is 6+2+5 = 13.<br><BR>\n" );
document.write( "Of course, if a formal algebraic solution is not required, the recognition that x^(1/4) is the square of x^(1/2) means we are looking for two integers, one the square of the other, whose sum is 30.  That obviously is 5 and 25, which means x is 5^4 = 35^2 = 625.<br><BR>\n" );
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