document.write( "Question 164204: 1.Find three consecutives odd integers such that the product of the first and third integers is 4 less than the square of the second integer.\r
\n" ); document.write( "\n" ); document.write( "2.The product of the two-digit no. and its tens digit is 54. Find the no. if the sum of the digits when added to the no. gives a result of 36.\r
\n" ); document.write( "\n" ); document.write( "i like math but it's hard(lol)!! \n" ); document.write( "
Algebra.Com's Answer #121036 by ankor@dixie-net.com(22740)\"\" \"About 
You can put this solution on YOUR website!
1. Find three consecutives odd integers such that the product of the first and
\n" ); document.write( " third integers is 4 less than the square of the second integer.
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\n" ); document.write( "Three odd integers: x, (x+2), (x+4)
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\n" ); document.write( "The product of 1st & 3rd, is 4 less than the 2nd squared
\n" ); document.write( "x(x+4) = (x+2)^2 - 4
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\n" ); document.write( "x^2 + 4x = x^2 + 4x + 4 - 4
\n" ); document.write( "x^2 + 4x = x^2 + 4x
\n" ); document.write( "Which is, of course true, but means there is not a unique solution
\n" ); document.write( "Pick any 3 odd consecutive numbers and this equation will be true
\n" ); document.write( "(It's also true for 3 consecutive even numbers)
\n" ); document.write( "Try it on your calc.
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\n" ); document.write( "2.The product of the two-digit no. and its tens digit is 54. Find the no.,
\n" ); document.write( " if the sum of the digits when added to the no. gives a result of 36.
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\n" ); document.write( "Let = 10x + y = the two digit number
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\n" ); document.write( "10's digit times the number = 54
\n" ); document.write( "x(10x+y) = 54
\n" ); document.write( "10x^2 + xy = 54
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\n" ); document.write( "number + sum of the digits = 36
\n" ); document.write( "(10x+y) + x + y = 36
\n" ); document.write( "11x + 2y = 36
\n" ); document.write( "2y = 36 - 11x
\n" ); document.write( "y = (18 - 5.5x); divided the equation by 2
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\n" ); document.write( "10x^2 + x(18-5.5x) = 54
\n" ); document.write( "10x^2 + 18x - 5.5x^2 = 54
\n" ); document.write( "10x^2 - 5.5x^2 + 18x = 54
\n" ); document.write( "4.5x^2 + 18x - 54 = 0; multiplied equation to get rid of the decimal
\n" ); document.write( "9x^2 + 36x - 108 = 0
\n" ); document.write( "simplify, divide by 9
\n" ); document.write( "x^2 + 4x - 12 = 0
\n" ); document.write( "(x + 6)(x - 2) = 0
\n" ); document.write( "x = -6
\n" ); document.write( "x = +2
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\n" ); document.write( "Let's just use the positive solution here; x = 2:
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\n" ); document.write( "Find y using the equation: x(10x+y) = 54, substitute 2 for x
\n" ); document.write( "2(10(2) + y)= 54
\n" ); document.write( "2(20 + y) = 54
\n" ); document.write( "40 + 2y = 54
\n" ); document.write( "2y = 54 - 40
\n" ); document.write( "2y = 14
\n" ); document.write( "y = 7
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\n" ); document.write( "The \"number\" is 27
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\n" ); document.write( "you can check the solutions in the two original equations
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