document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1210429>Question 1210429</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1) Solve 2(√4x+5) - (√3x+1) = 6, where x is an integer.\r<BR>\n" );
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document.write( "2) Given that sinx = -3/5, where 180° ≤ x ≤ 270° and cos y = - 15/17 , where 90° ≤ y ≤ 180°. find the value of tan(x-y).<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #852519 by </B><A HREF=/tutors/aboutme.mpl?userid=n2><B>n2(19)</B></A><img src=\"/images/stars/stars-06.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=n2><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=852519\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( "1) Solve 2(√4x+5) - (√3x+1) = 6, where x is an integer.<BR>\n" );
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document.write( "Tutor @greenestamps made a great step forward, guessing or finding mentally <BR>\n" );
document.write( "one integer solution &nbsp;x = 5.\r<BR>\n" );
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document.write( "But when a solution to a Math problem, &nbsp;or a math equation is found by the &nbsp;\" trial and error \"<BR>\n" );
document.write( "guessing method, &nbsp;always a question arises - whether this solution is unique or whether other solutions exist.\r<BR>\n" );
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document.write( "There is one brilliant reasoning, &nbsp;which may help in some cases,<BR>\n" );
document.write( "and it will help to answer for this given equation.\r<BR>\n" );
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document.write( "Notice that in the left side of the equation the term &nbsp;<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%284x%2B1%29 ALIGN=MIDDLE  ALT=\"sqrt%284x%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  &nbsp;grows &nbsp;FASTER &nbsp;than<BR>\n" );
document.write( "the other term, &nbsp;<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%283x%2B1%29 ALIGN=MIDDLE  ALT=\"sqrt%283x%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.   &nbsp;&nbsp;&nbsp;&nbsp;(This is obvious).\r<BR>\n" );
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document.write( "AFORTIORI, &nbsp;the term &nbsp;<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Asqrt%284x%2B1%29 ALIGN=MIDDLE  ALT=\"2%2Asqrt%284x%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  &nbsp;grows even &nbsp;FASTER &nbsp;than the other term, &nbsp;<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%283x%2B1%29 ALIGN=MIDDLE  ALT=\"sqrt%283x%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "It means that the left side of the given equation is a monotonic function of &nbsp;x<BR>\n" );
document.write( "(monotonically increases for positive values of &nbsp;x).\r<BR>\n" );
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document.write( "Hence, &nbsp;this given equation, &nbsp;having a constant value in its right side, &nbsp;has a &nbsp;UNIQUE &nbsp;solution.\r<BR>\n" );
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document.write( "In other words - if it has one solution, &nbsp;then this solution is unique.\r<BR>\n" );
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document.write( "Reasoning this way, &nbsp;we transform our &nbsp;\" trial and error \" &nbsp;guessing method into &nbsp;MATHEMATICALLY &nbsp;STRICT &nbsp;&nbsp;<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28highlight%28proof%29%29 ALIGN=MIDDLE  ALT=\"highlight%28highlight%28proof%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "So, &nbsp;x = 5 &nbsp;is the unique real and integer solution to this given equation.\r<BR>\n" );
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document.write( "       Be careful !  That is true that in the positive 'x'-domain the left side monotonically increases.\r\n" );
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document.write( "       But what about negative 'x' ? - In this problem, the domain of negative 'x' is small and does not \r\n" );
document.write( "       make influence to the final conclusion !\r\n" );
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