document.write( "Question 1013376: 2 numbers whose sum is 10 and the sum of their squares is a minimum. If x is the first number, express the minimum as a function of x and find the numbers. \n" ); document.write( "

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\n" ); document.write( "2 numbers whose sum is 10 and the sum of their squares is a minimum.
\n" ); document.write( "If x is the first number, express the minimum as a function of x and find the numbers.
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\n" ); document.write( "\n" ); document.write( "Answer. The numbers are 5 and 5.\r
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document.write( "Proof\r\n" );
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document.write( "Let x be one number, then the other is 10-x.\r\n" );
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document.write( "The sum of their squares is \r\n" );
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document.write( " =  =  =  = .\r\n" );
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document.write( "One can see that this quadratic function has the minimum at x = 5, and this minimum is equal to 50.\r\n" );
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document.write( "Thus we proved that one number, which gives the maximum, is 5.\r\n" );
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document.write( "Then the other number is 5 also.\r\n" );
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