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Let n be the lower number then the higher number is n + 1.
n (n + 1 ) = 552 : n² + n - 552 = 0
Solving for the roots of a quadratic equation gives :-
n = [-1 ± √(1 + 2208)] ÷ 2 = [-1 ± √2209] ÷ 2 = [-1 ± 47]÷ 2
Taking just the positive root gives n = -½ + 23½ = 23
The two consecutive numbers are therefore 23 and 24.
Whilst this is a very accurate but complicated process a much quicker result can be achieved by taking the square root of 552 = 23.5 (approx). Two consecutive numbers producing 552 must lie either side of the square root. A simple multiplication will reveal that the numbers are 23 and 24.
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