three consecutive positive integers are such that the sum of the square of the first and the product of the other two is 46 find the integers
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Assume 3 positive integers p, p + 1 and p + 2
★Situation
p² + (p + 1)(p + 2) = 46
2p² + 3p + 2 - 46 = 0
2p² + 3p - 44 = 0
2p² - 8p + 11p - 44 = 0
2p(p - 4) + 11(p - 4) = 0
(2p + 11)(p - 4) = 0
p = 4
★Therefore integers are 4,5 and 6
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