SOLUTION: find three consective intergers such that the product of the two smaller integers is 2 more than 10 times the largest integer.

Question 313297: find three consective intergers such that the product of the two smaller integers is 2 more than 10 times the largest integer.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
find three consecutive integers such that the product of the two smaller integers is 2 more than 10 times the largest integer.
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1st: x
2nd: x+1
3rd: x+2
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INEQUALITY:
x(x+1) > 10(x+2) + 2
x^2+x > 10x+22
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x^2-9x-22 > 0
(x-11)(x+2) > 0
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1st: Plot the boundary points of the inequality.
Draw a number line and plot x = -2 and x = 11
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Check a test value from each of the intervals in the INEQUALITY:
If x=-3, (-3)^2-9(-3)-22>0 ; true so solutions in (-inf,-2)
If x = 0, (0)^2-9(0)-22>0 ; false
If x = 12, (12)^2-9(12)-22>0 ; true so solutions in (11,+inf)
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Cheers,
Stan H.
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