document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=764376>Question 764376</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 9x to the fourth power minus 25x to the second power plus 16 is equal to zero </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #465403 by </B><A HREF=/tutors/aboutme.mpl?userid=DrBeeee><B>DrBeeee(684)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=DrBeeee><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=465403\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Given:<BR>\n" );
document.write( "(1) 9x^4 - 25x^2 + 16 = 0<BR>\n" );
document.write( "Let<BR>\n" );
document.write( "(2) y = x^2  in (1) and get<BR>\n" );
document.write( "(3) 9y^2 - 25y + 16 = 0 which factors into<BR>\n" );
document.write( "(4) (9y - 16)*(y - 1) = 0<BR>\n" );
document.write( "FOIL (4) to get<BR>\n" );
document.write( "(5) 9y*y - 9y - 16y + 16 = 0 or<BR>\n" );
document.write( "(6) 9y^2 - 25y + 16 = 0 which is the same as (3)<BR>\n" );
document.write( "Setting each factor of (4) equal to zero yields<BR>\n" );
document.write( "(7) 9y - 16 = 0 or<BR>\n" );
document.write( "(8) y = 16/9 and<BR>\n" );
document.write( "(9) y - 1 = 0 or<BR>\n" );
document.write( "(10) y = 1<BR>\n" );
document.write( "But from (2) we have<BR>\n" );
document.write( "(11) x^2 = 16/9 or<BR>\n" );
document.write( "(12) x = +-4/3 and<BR>\n" );
document.write( "(13) x^2 = 1 or<BR>\n" );
document.write( "(14 x = +-1<BR>\n" );
document.write( "Therefore, as expected for a fourth order equation we get four roots<BR>\n" );
document.write( "(15) x = {-4/3,-1,1,4/3}<BR>\n" );
document.write( "Put each value of x of (15) into (1) to check.<BR>\n" );
document.write( "Is (9(-4/3)^4 - 25(-4/3)^2 + 16 = 0)?<BR>\n" );
document.write( "Is (9(256/81) - 25(16/9) + 16 = 0)?<BR>\n" );
document.write( "Is (256/9 - 400/9 + 16 = 0)?<BR>\n" );
document.write( "Is ((-144)/9 + 16 = 0)?<BR>\n" );
document.write( "Is (-16 + 16 = 0)?<BR>\n" );
document.write( "Is (0 = 0)? Yes<BR>\n" );
document.write( "Is (9(-1)^4 - 25(-1)^2 + 16 = 0)?<BR>\n" );
document.write( "Is (9 - 25 + 16 = 0)?<BR>\n" );
document.write( "Is (-16 + 16 = 0)?<BR>\n" );
document.write( "Is (0 = 0)? Yes<BR>\n" );
document.write( "Is (9(1)^4 - 25(1)^2 + 16 = 0)?<BR>\n" );
document.write( "Is (9 - 25 + 16 = 0)?<BR>\n" );
document.write( "Is (-16 + 16 = 0)?<BR>\n" );
document.write( "Is (0 = 0)? Yes<BR>\n" );
document.write( "Is (9(4/3)^4 - 25(4/3)^2 + 16 = 0)?<BR>\n" );
document.write( "Is (9(256/81) - 25(16/9) + 16 = 0)?<BR>\n" );
document.write( "Is (256/9 - 400/9 + 16 = 0)?<BR>\n" );
document.write( "Is ((-144)/9 + 16 = 0)?<BR>\n" );
document.write( "Is (-16 + 16 = 0)?<BR>\n" );
document.write( "Is (0 = 0)? Yes<BR>\n" );
document.write( "Answer: x = {-4/3,-1,1,4/3}<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );