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Find two consecutive positive integers whose product is 34 more than their sum?
Wiki User
∙ 13y ago
I don't think there's a solution to this problem. Let's work it through.
Two consecutive integers: x & y. So y = x + 1.
Product is 34 more than sum. Product (x*y) = sum(x+y) +34
Substitute [y=x+1] into second equation: x*(x+1) = x + (x+1) + 34
x2 + x = x + x + 1 + 34 --> x2 + x - 2*x - 35 = 0 --> x2 - x - 35 = 0 (quadratic)
In the quadratic formula: a = 1, b = -1, c = -35, so we have (1 ± sqrt[1 - 4*(-35)])/(2*1) = (1 ± sqrt(141))/2; sqrt(141) is irrational, so the solution is not integers. Someone else can maybe check my work.
Wiki User
∙ 13y ago
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