The sum of the two numbers is 46, and the sum of their squares is 1130. Find these numbers.

The sum of the two numbers is 46, and the sum of their squares is 1130. Find these numbers. Please help me solve, I climbed a bunch of sites and similar questions, but I still do not understand where the number 92y comes from. Here is the beginning of my solution: Let x be the first number, y the second number. It is known that x + y = 46 and x2 + y2 = 1130. Let’s compose and solve a system of equations.

We immediately introduce two variables:

Let m be the first number and n the second.

Based on the conditions of the problem, we will compose and solve a system of two equations with two unknowns:

m + n = 46;

m ^ 2 + n ^ 2 = 1130;

You can solve it in different ways, we will solve it by the substitution method – we will express one of the variables in the first equation of the system, after which we will substitute the expression in the second equation:

n = 46-m;

m ^ 2 + (46 – m) ^ 2 = 1130;

m ^ 2 + 2116 – 92 * m + m ^ 2 – 1130 = 0;

2 * m ^ 2 – 92 * m + 986 = 0;

m ^ 2 – 46 * m + 493 = 0;

D = 2116-1972 = 144;

m1 = (46 – 12) / 2 = 17;

m2 = (46 + 12) / 2 = 29.

Our numbers are 17 and 29.