document.write( "Question 1125614: Among all pairs of numbers (x,y) such that 4x+y=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 #741911 by ikleyn(52806)\"\" \"About 
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document.write( "They want you find the minimum of this quadratic function\r\n" );
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document.write( "    f(x) = \"x%5E2\" + \"%2818-4x%29%5E2\" = \"x%5E2+%2B+324+-+144x+%2B+16x%5E2\" = \"17x%5E2+-+144x+%2B+324\".\r\n" );
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document.write( "For the general form of a quadratic function  y = ax^2 + bx + c  the minimum is achieved at  x = \"-b%2F%282a%29\".\r\n" );
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document.write( "In your case the minimum is at  x= \"-+%28-144%29%2F%282%2A17%29\" = \"72%2F17\".\r\n" );
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document.write( "The pair under the question is  x = \"72%2F17\",  y = \"18+-+4%2A%2872%2F17%29\" = \"18%2F17\".\r\n" );
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