document.write( "Question 405827: what multiplied by what gives you 54 and adds up 21 \n" ); document.write( "

Algebra.Com's Answer #286573 by richard1234(7193) $\"\"$ $\"About$

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I think you want two numbers x and y such that\r
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\n" ); document.write( "\n" ); document.write( "xy = 54
\n" ); document.write( "x+y = 21\r
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\n" ); document.write( "\n" ); document.write( "Two ways to do this:\r
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\n" ); document.write( "\n" ); document.write( "If you can factor 54 in your head, and know that 54 = 18*3, you can conclude that 18 and 3 are the numbers.\r
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\n" ); document.write( "\n" ); document.write( "Or, letting y = 21 - x (from the second equation, we substitute and obtain a quadratic:\r
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\n" ); document.write( "\n" ); document.write( " $\"x%2821+-+x%29+=+54\"$ --> $\"-x%5E2+%2B+21x+-+54+=+0\"$ --> $\"x%5E2+-+21x+%2B+54+=+0\"$ . Either by the quadratic formula or by factoring we get x = 18 or x = 3, and both these solutions are equivalent since one implies the other. \n" ); document.write( "

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