document.write( "Question 1051078: maximize q=5xy^2, where x and y are positive numbers such that x+y^2=8 \n" ); document.write( "

Algebra.Com's Answer #666669 by ikleyn(52787) $\"\"$ $\"About$

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\n" ); document.write( "maximize q=5xy^2, where x and y are positive numbers such that x+y^2=8
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\n" ); document.write( "\n" ); document.write( "The solution at the Algebra level, with no calculus.\r
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document.write( "Substitute into q equation,\r\n" );
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document.write( "Now q is a function of one variable, y.\r\n" );
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document.write( "q = .\r\n" );
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document.write( "\"Complete the square\" :\r\n" );
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document.write( "q =  =  =  + .\r\n" );
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document.write( "It shows that q is maximal at   = 4,  or  y = +/-2.\r\n" );
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document.write( "According to the condition, only positive \"y\" are considered, so the solution is y=2.\r\n" );
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document.write( "Then x = 4.\r\n" );
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document.write( "The minimum of q is 80.\r\n" );
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