document.write( "Question 1070500: The sum of two numbers is 8. Find the numbers if the sum of their squares is a minimum. (hint completing the square) \n" ); document.write( "

Algebra.Com's Answer #685584 by ikleyn(52756) $\"\"$ $\"About$

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\n" ); document.write( "The sum of two numbers is 8. Find the numbers if the sum of their squares is a minimum. (hint completing the square)
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document.write( "Let x be one of the two numbers.\r\n" );
document.write( "Then the other number is 8-x, and the sum of their squares is\r\n" );
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document.write( "  q(x) =      (1)\r\n" );
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document.write( "=  = .\r\n" );
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document.write( "This quadratic function has the minimum at x =  =  =  = 4.\r\n" );
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document.write( "Calculate this maximum value. For it, substitute the value x= 4 into the function (1):\r\n" );
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document.write( "q(4) =  = 16 + 16 = 32.\r\n" );
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document.write( "Answer. The minimum is achieved at x = 4 and is equal to 16.\r\n" );
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document.write( "               The vertex of the quadratic function is (4,16).\r\n" );
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\n" ); document.write( "\n" ); document.write( "On finding the maximum/minimum of a quadratic function see the 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
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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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