document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=767154>Question 767154</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If ab=10 and a^2+b^2=30, then solve for y in y=(a+b)^2 . Can someone please explain how you get the answer step by step please especially how you multiply the right side. Thanks </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #467450 by </B><A HREF=/tutors/aboutme.mpl?userid=tinbar><B>tinbar(133)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=tinbar><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=467450\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You can solve for a and b uniquely and then plug those values into the expression for y OR you could be a mathematical boss and do it this way:\r<BR>\n" );
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document.write( "(a+b)^2 ... What is this really? It's just (a+b) * (a+b) = (a^2) + (2ab) + (b^2)\r<BR>\n" );
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document.write( "But hey, you already have a value for (ab) and a value for a^2+b^2!!\r<BR>\n" );
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document.write( "So if ab = 10, then 2ab = 2*10 = 20. We need not do anything for a^2+b^2, it's given to us in the form we want.\r<BR>\n" );
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document.write( "So now we just add, 20 + 30 = 50! ... Like a boss ;)\r<BR>\n" );
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document.write( "Alternative solution:\r<BR>\n" );
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document.write( "ab= 10 <=> a = 10/b<BR>\n" );
document.write( "plug this value of a into second equation<BR>\n" );
document.write( "(10/b)^2 + b^2 = 30<BR>\n" );
document.write( "100/b^2 + b^2 = 30<BR>\n" );
document.write( "(100 + b^4) = 30 * b(^2)<BR>\n" );
document.write( "b^4 - 30b^2 + 100 = 0\r<BR>\n" );
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document.write( "replace b^2 with some arb variable for now, like c, so that we can use quadratic formula to solve for c, then we can solve for b\r<BR>\n" );
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document.write( "c^2 - 30c + 100 = 0 Now just use quadratic formula to find values of c<BR>\n" );
document.write( "which should be c = 5 (3+sqrt(5)) and another value where c is negative, but we will ignore this one since to find b, we need to square root c, and we can't do that for negative values.\r<BR>\n" );
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document.write( "so then b = sqrt(c), from this you can solve a, and finally solve y, but this is horribly ugly and long and very very NOT boss like </SPAN>\n" );
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