The sum and product of three whole numbers is equal. Find that three whole numbers

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Solution

Let the three whole number are x, x+1, x+2.
product = sum
$x \times (x + 1) \times x + 2 = x + x + 1 + x + 2 x \times (x + 1) \times (x + 2) = 3 x + 3 x \times (x + 1) \times (x + 2) = 3 (x + 1) x \times (x + 2) = 3 x^{2} + 2 x = 3 x^{2} + 2 x = 3 x^{2} - x + 3 x - 3 = 0 x (x - 2) + 3 (x - 1) = 0 (x - 1) (x + 3) = 0 (x - 1) = 0 x = 1$
and
$(x + 3) = 0 x = - 3 x = 1, - 3$
For whole number we take only x=2
put the value of x in $x, x + 1, x + 2$
$x = 1 x + 1 = 1 + 1 = 2 x = 2 = 1 + 2 = 3$
Hence number are 1, 2, 3

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