Answer :

Let the three consecutive positive integers be

(x – 1), xand (x + 1)

x^{2} + 1 – 2x + x^{2} + x = 46

2x^{2} – x – 45 = 0

2x^{2} – 10x + 9x – 45 = 0

2x(x – 5) + 9(x – 5) = 0

(x = 5)(2x + 9) = 0

x = 5,

Since, x are positive

∴ neglecting

∴ Integers

x – 1 = 5 – 1 = 4, x = 5

x + 1 = 5 + 1 = 6

∴ Required integers are 4, 5 and 6.

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