document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1208228>Question 1208228</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If a + b = 1 and a⁴ + b⁴ = 17. <BR>\n" );
document.write( "Find a,b </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #846517 by </B><A HREF=/tutors/aboutme.mpl?userid=mananth><B>mananth(16946)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=mananth><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=mananth><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=846517\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If a + b = 1 and a⁴ + b⁴ = 17.\r<BR>\n" );
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document.write( "If a + b = 1 and a⁴ + b⁴ = 17.\r<BR>\n" );
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document.write( "(a+b)=1<BR>\n" );
document.write( "square the equation\r<BR>\n" );
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document.write( "(a+b)^2=1\r<BR>\n" );
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document.write( "a^2+2ab+b^2=1\r<BR>\n" );
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document.write( "a^2+b^2=1-2ab\r<BR>\n" );
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document.write( "Now \r<BR>\n" );
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document.write( "a^4+b^4=17  (given)\r<BR>\n" );
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document.write( "use identity\r<BR>\n" );
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document.write( "(a^2+b^2)^2 -2a^2b^2=17\r<BR>\n" );
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document.write( "(1-2ab)^2 -2(ab)^2=17\r<BR>\n" );
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document.write( "1-4ab+4a^2b^- 2(ab)^2=17\r<BR>\n" );
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document.write( "-4ab+2(ab)^2=16\r<BR>\n" );
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document.write( "2a^2b^2 -4ab-16=0\r<BR>\n" );
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document.write( "2(ab)^2-4ab-16=0\r<BR>\n" );
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document.write( "compare with ax^2+bx+c=0\r<BR>\n" );
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document.write( "here a = 2 b=-4 c= -16\r<BR>\n" );
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document.write( "Use formula method\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+%28-b+%2B-sqrt%28b%5E2-4ac%29%29%2F+2a+ ALIGN=MIDDLE  ALT=\"+x+=+%28-b+%2B-sqrt%28b%5E2-4ac%29%29%2F+2a+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "b^2-4ac = 16 +128=144\r<BR>\n" );
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document.write( "ab =( 4+12)/4     OR   4  -12/4<BR>\n" );
document.write( "ab = 4   or -2\r<BR>\n" );
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document.write( "Now <BR>\n" );
document.write( "If ab = 4<BR>\n" );
document.write( "a= 4/b\r<BR>\n" );
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document.write( "a+b=1 (given)<BR>\n" );
document.write( "substitute a<BR>\n" );
document.write( "4/b +b=1<BR>\n" );
document.write( "Multiply by b\r<BR>\n" );
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document.write( "4+b^2=b\r<BR>\n" );
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document.write( "b^2-b+4 =0\r<BR>\n" );
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document.write( "the discriminant is <0 no real roots\r<BR>\n" );
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document.write( "When ab =-2<BR>\n" );
document.write( "a+b=1\r<BR>\n" );
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document.write( "ab =-2\r<BR>\n" );
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document.write( "b= -2/a\r<BR>\n" );
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document.write( "a-2/a = 1<BR>\n" );
document.write( "Multiply by a\r<BR>\n" );
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document.write( "a^2-2=a\r<BR>\n" );
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document.write( "a^2-a-2=0<BR>\n" );
document.write( "Use quadratic formula <BR>\n" );
document.write( "we get\r<BR>\n" );
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document.write( "a=2  or -1\r<BR>\n" );
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document.write( "Plug a in a+b =1 find b  for both values of a\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );