Answer :
Let the three consecutive positive integers be x, x + 1, x + 2
According to the given condition,
x2 + (x + 1)(x + 2) = 46
x2 + x2 + 3x + 2 = 46
2x2 + 3x – 44 = 0
Using the splitting middle term – the middle term of the general equation is divided in two such values that:
Product = a.c
For the given equation a = 2 b = 3 c = – 44
= 2. – 44 = – 88
And either of their sum or difference = b
= 3
Thus the two terms are 11 and – 8
Sum = 11 – 8 = 3
Product = 11. – 8 = – 88
2x2 + 3x – 44 = 0
2x2 + 11x – 8x – 44 = 0
x(2x + 11) – 4(2x + 11) = 0
(2x + 11)(x – 4) = 0
x = 4 or – 11/2
x = 4 (x is a positive integers)
When x = 4
x + 1 = 4 + 1 = 5
x + 2 = 4 + 2 = 6
Hence the required integers are 4, 5, 6
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