Present the number 123 as a sum of terms, the product of which is equal to a given number.

Let us denote this number by A, and the required terms by x and y.

By the condition of the problem, we have:

x + y = 123,

x * y = A.

From the first equation we get: y = 123 – x.

Therefore, we have:

x * y = x * (123 – x) = A,

x ^ 2 – 123 * x + A = 0.

We got a quadratic equation:

Discriminant D = (b ^ 2 – 4 * a * c) = 123 ^ 2 – 4 * A.

x1 = (123 – √ (123 ^ 2 – 4 * A)) / 2,

x2 = (123 + √ (123 ^ 2 + 4 * A)) / 2.

From here we get:

y1 = 123 – x1 = 123 – (123 – √ (123 ^ 2 – 4 * A)) / 2) = (123 + √ (123 ^ 2 – 4 * A)) / 2 = x2,

y2 = 123 – x2 = 123 – (123 + √ (123 ^ 2 – 4 * A)) / 2 = (123 – √ (123 ^ 2 – 4 * A)) / 2 = x1.

Thus, the required terms:

x = (123 – √ (123 ^ 2 – 4 * A)) / 2,

y = (123 + √ (123 ^ 2 – 4 * A)) / 2.

Note that a necessary condition for the existence of a decomposition into terms is:

D> = 0,

123 ^ 2 – 4 * A> = 0,

A <= 123 ^ 2/4.