Find a two-digit number if you know that its sum is 5 and their product is 4.

Let’s make an equation.

Let x be one of the digits of a two-digit number, then y is another digit of a two-digit number.

The sum of the digits is 5, which means: x + y = 5, and the product: x * y = 4.

Let’s solve the resulting system of equations.

Let us express the variable x from the first equality: x = 5 – y.

Let’s substitute the value of x in the second equality:

(5 – y) * y = 4.

5 * y – y ^ 2 = 4.

5 * y – y ^ 2 – 4 = 0.

y ^ 2 – 5 * y + 4 = 0.

Let’s solve the quadratic equation.

D = (-5) ^ 2 – 4 * 1 * 4 = 25 – 16 = 9.

y1 = (5 – √9) / (2 * 1) = (5 – 3) / 2 = 2/2 = 1.

y2 = (5 + √9) / (2 * 1) = (5 + 3) / 2 = 8/2 = 4.

x1 = 5 – 1 = 4.

x2 = 5 – 4 = 1.

Let’s check the fulfillment of the problem conditions for х1 = 4 and у1 = 1.

4 + 1 = 5; 5 = 5.

4 * 1 = 4; 4 = 4.

The system of equations is fulfilled x1 = 4 and y1 = 1 are the solution to the system.

Let us check the fulfillment of the problem conditions for x2 = 1 and y2 = 4.

1 + 4 = 5; 5 = 5.

1 * 4 = 4; 4 = 4.

The system of equations is fulfilled x2 = 1 and y1 = 4 are also a solution to the system.

Answer: the conditions of the problem are satisfied by the number 14 or 41.