document.write( "Question 1136263: Among all pairs of numbers (x,y) such that 8x+2y=18, find the pair for which the sum of squares, x2+y2, is minimum. Write your answers as fractions reduced to lowest terms. \n" ); document.write( "

Algebra.Com's Answer #754042 by ikleyn(52794) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "\n" ); document.write( "            Really, such a problem can stump unexperienced student.\r
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\n" ); document.write( "\n" ); document.write( "            The solution is as follows.\r
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document.write( "From equation  8x + 2y = 18, express  y =  = -4x + 9  and substitute it into the expression  \r\n" );
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document.write( "    f(x,y) =  =  =  = .     (1)\r\n" );
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document.write( "Now your function is presented as a quadratic function of ONE argument.\r\n" );
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document.write( "You can easily find its minimum by using this very well known shortcut    = \"  \".\r\n" );
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document.write( "In this case  a = 17 and b = -72,  so   =  = .\r\n" );
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document.write( "So, you just know the value of \" x \" where the function has the minimum.\r\n" );
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document.write( "By knowing  ,  you can easily calculate   = . \r\n" );
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document.write( "I leave this simple arithmetic for you to complete it on your own.\r\n" );
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\n" ); document.write( "\n" ); document.write( "On finding the maximum/minimum of a quadratic function see my lessons \r
\n" ); document.write( "\n" ); document.write( "    - HOW TO complete the square to find the minimum/maximum of a quadratic function\r
\n" ); document.write( "\n" ); document.write( "    - Briefly on finding the minimum/maximum of a quadratic function\r
\n" ); document.write( "\n" ); document.write( "    - HOW TO complete the square to find the vertex of a parabola\r
\n" ); document.write( "\n" ); document.write( "    - Briefly on finding the vertex of a parabola\r
\n" ); document.write( "\n" ); document.write( "in this site.\r
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\n" ); document.write( "\n" ); document.write( "Also, you have this free of charge online textbook in ALGEBRA-I in this site\r
\n" ); document.write( "\n" ); document.write( "    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.\r
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\n" ); document.write( "\n" ); document.write( "The referred lessons are the part of this textbook under the topic \"Finding minimum/maximum of quadratic functions\". \r
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\n" ); document.write( "\n" ); document.write( "Save the link to this online textbook together with its description\r
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\n" ); document.write( "\n" ); document.write( "Free of charge online textbook in ALGEBRA-I
\n" ); document.write( "https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson\r
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\n" ); document.write( "\n" ); document.write( "to your archive and use it when it is needed.\r
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