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 #852516 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13250)</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=852516\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "For the first problem....<br><BR>\n" );
document.write( "NOTE: Don't use \"√\" when posting problems involving square roots -- or, if you do, enclose the expressions under the radicals in parentheses.  \"2(√4x+5)\" looks like <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2sqrt%284x%29%2B5 ALIGN=MIDDLE  ALT=\"2sqrt%284x%29%2B5\"   DISABLED_style= \"max-width:90%; height:auto;\" >, when apparently the intended expression is 2(√(4x+5)) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2sqrt%284x%2B5%29 ALIGN=MIDDLE  ALT=\"2sqrt%284x%2B5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Outline for a formal solution....<BR>\n" );
document.write( "(1) rewrite the equation with one radical on each side<BR>\n" );
document.write( "(2) square both sides of that equation; you will still have a radical on one side<BR>\n" );
document.write( "(3) isolate that radical on one side and again square both sides of the equation, resulting finally in an equation without any radicals<br><BR>\n" );
document.write( "If you do all that algebra correctly, you will end up with this quadratic equation: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=169x%5E2-874x%2B145=0 ALIGN=MIDDLE  ALT=\"169x%5E2-874x%2B145=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Options for what to do from here....<br><BR>\n" );
document.write( "(1) solve that equation by factoring (have fun!!!)<BR>\n" );
document.write( "(2) solve the equation using the quadratic formula (perhaps even MORE fun!!!!)<BR>\n" );
document.write( "(3) solve the equation using a graphing calculator (e.g., TI84 or equivalent; or online at desmos.com)<BR>\n" );
document.write( "Option (3) is much less work than either of the other options....<br><BR>\n" );
document.write( "But if you are going to solve the problem using technology, why bother with the algebra outlined above?  Simply use a graphing utility to graph the expressions on each side of the original equation and find the x value where the graphs intersect.<br><BR>\n" );
document.write( "Finally, what is the easiest (and by far the fastest) way to solve the problem?<br><BR>\n" );
document.write( "Assume the answer is a whole number; ignore ALL of the above and look for whole number values of x for which (4x+5) and (3x+1) are both perfect squares.<br><BR>\n" );
document.write( "ANSWER: x = 5<br><BR>\n" );
document.write( "CHECK: 2*sqrt(4x+5)-sqrt(3x+1) = 2*sqrt(25)-sqrt(16) = 2(5)-4 = 10-4 = 6<br><BR>\n" );
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