document.write( "Question 194616: one number is 30 less that twice another number. find the 2 numbers if the sum of their squares is a minimum. \n" ); document.write( "

Algebra.Com's Answer #146015 by RAY100(1637) $\"\"$ $\"About$

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let n=2m -30
\n" ); document.write( "and n^2 + m^2 = min
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\n" ); document.write( "(2m-30)^2 +m^2 =0
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\n" ); document.write( "4m^2 -120m +90 +m^2 =0
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\n" ); document.write( "3m^2 -120 m +90 =0
\n" ); document.write( "3(m^2 -40m +30 ) =0
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\n" ); document.write( "use quadratic eqn , a=3, b=-40,c=30
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\n" ); document.write( "m= ( -(-40) +/- sqrt( -(-40) - 4 (1)(30) ) / 2(1)
\n" ); document.write( "m = (40 +/- sqrt (1600-120) )/2
\n" ); document.write( "m= (40 +/- 38.47) /2 = 39.2 ,,,, or .765
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\n" ); document.write( "subst for n,
\n" ); document.write( "n= 2m-30 = 2*39.2 -30 = 48.4
\n" ); document.write( "or n= 2* .765 -30 = 28.47
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\n" ); document.write( "pairs are m= 39.2, n=48.4
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\n" ); document.write( ",,,,,,,,m=.765, n= 28.47
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\n" ); document.write( "problem asks that sum of squares is a minimum, therefore use, m=.765, n=28.47 \n" ); document.write( "

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