document.write( "Question 884520: Find 3 consecutive odd numbers where the product of the smaller two numbers is 46 less than the square of the largest number. \n" ); document.write( "
Algebra.Com's Answer #534373 by algebrapro18(249)\"\" \"About 
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Well consecutive numbers come one after the next. So 3 consecutive odd numbers would be like 1,3,5 or 3,5,7. Notice the difference between the numbers is two. So to go from 1 to the next we just take the first number and add 2. Writing this algebraically we get:
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\n" ); document.write( "\n" ); document.write( "Number 1 = x
\n" ); document.write( "Number 2 = x+2
\n" ); document.write( "Number 3 = x+2+2 = x+4
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\n" ); document.write( "\n" ); document.write( "So now we need to find 3 consecutive odd numbers such that the product of the smaller two numbers is 46 less than the square of the largest number. The smallest two numbers above are x and x+2 and the largest number would be x+4. Writing this algebraically we get:
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\n" ); document.write( "\n" ); document.write( "x(x+2)=(x+4)^2-46
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\n" ); document.write( "\n" ); document.write( "Now we just plug and chug to solve for x.
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\n" ); document.write( "\n" ); document.write( "x(x+2)=(x+4)^2-46
\n" ); document.write( "x^2+2x = (x+4)(x+4)-46
\n" ); document.write( "x^2+2x = x^2+4x+4x+16-46
\n" ); document.write( "x^2+2x = x^2+8x+16-46
\n" ); document.write( "x^2+2x = x^2+8x-30
\n" ); document.write( "0 = x^2-x^2+8x-2x-30
\n" ); document.write( "0 = 6x-30
\n" ); document.write( "30 = 6x
\n" ); document.write( "5 = x
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\n" ); document.write( "\n" ); document.write( "So we know that the first number is 5. Plugging back into our equations gives us the final answer of:
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\n" ); document.write( "\n" ); document.write( "Number 1 = x = 5
\n" ); document.write( "Number 2 = x+2 = 5+2 = 7
\n" ); document.write( "Number 3 = x+2+2 = x+4 = 5+4 = 9
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