# The product of two natural numbers is 154, and the sum of their square is 317. Find these numbers.

August 31, 2021 | education

| To solve the problem, you can compose a system of equations, and as it is known that the product of two numbers is 154, and the sum of their squares is 317. Let’s denote the numbers x and y:

x * y = 154

x² + y² = 317;

x = 154 / y

y⁴ – 317y² + 23716 = 0.

Let’s set z = y² and get the usual quadratic equation:

z² – 317z + 23716 = 0;

z₁ = 196; z₂ = 121;

y₁ = 14; y₂ = 11.

x₁ = 11; x₂ = 14.

Answer: x and y have two solutions: y₁ = 14; y₂ = 11; x₁ = 11; x₂ = 14.

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