If one of the numbers is x, then the other number is x + 2. So,
x(x + 2) = 399
x^2 + 2x = 399 Complete the square by adding 1 at both sides ;
x^2 + 2x + 1 = 399 + 1 Use the formula: (a + b)^2 = a^2 + 2ab + b^2
(x + 1)^2 = 400
x + 1 = (+ & - )(square root of 400) subtract 1 to both sides
x = -1 (+ & -) 20
x = -1 + 20 or x = -1 - 20
x = 19 or x = -21
So,
x + 2 = 19 + 2 = 21 or x + 2 = - 21 + 2 = - 19
Thus the numbers are:
19 and 21 or -19 and - 21
Check:
(19)(21) = 399
(-19)(-21) = 399
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Find 3 consecutive numbers where the product of the smaller two numbers is 19 less than the square of the largest number.
The numbers are -16 and -15.