document.write( "Question 766392: find the smallest of 3 consecutive positive integers such that when 5 times the largest is subtracted from the square of the middle one the result exceeds three times the smallest by 7.\r
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Algebra.Com's Answer #466949 by ramkikk66(644) $\"\"$ $\"About$

You can put this solution on YOUR website!

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document.write( "Question:
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document.write( "find the smallest of 3 consecutive positive integers such that when 5 times the largest is subtracted from the square of the middle one the result exceeds three times the smallest by 7.
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document.write( "Ans:\r
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document.write( "Let the numbers be n and (n+1) and (n+2)\r
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document.write( "(You can also assume n-1, n and n+1 - the approach is still the same)\r
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document.write( "Now let's look at each part of the question and translate it into algebraic form.\r
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document.write( "Largest number = n+2
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document.write( "5 times the largest number =  = \r
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document.write( "Middle number = n+1
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document.write( "Square of the middle number = \r
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document.write( "Smallest number = n
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document.write( "3 times the smallest number = \r
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document.write( "\"5 times largest number\" subtracted from \"square of middle number\" will give you\r
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document.write( " = \r
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document.write( "This value \"exceeds '3 times the smallest' by 7\" means this is equal to 
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document.write( "\"3 times the smallest + 7\" i.e. it is \r
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document.write( "Equating the above, \r
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document.write( "i.e. 
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document.write( "This is a standard quadratic equation, which can be solved by factorization or
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document.write( "by the quadratic formula, as shown below.\r
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document.write( "The solutions are n = 8, or n = -2\r
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document.write( "Since it is given that the numbers are positive, the set of 3 numbers are
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document.write( "8,9 and 10.\r
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document.write( "Check: Square of middle number - 5 times largest number = 81 - 50 = 31
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document.write( "3 times smallest number = 3 * 8 = 24.
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document.write( "31 exceeds 24 by 7 - correct!\r
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document.write( ":)
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document.write( "Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation  (in our case ) has the following solutons:
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document.write( "  For these solutions to exist, the discriminant  should not be a negative number.
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document.write( "  
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document.write( "  First, we need to compute the discriminant : .
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document.write( "  
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document.write( "  Discriminant d=100 is greater than zero. That means that there are two solutions: .
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document.write( "    
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document.write( "    Quadratic expression  can be factored:
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document.write( "  
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document.write( "  Again, the answer is: 8, -2.\n" );
document.write( "Here's your graph:
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