If each edge of the cube is increased by 3, then its total surface area will increase ea 126. Find the edge of the cube.

1. Let the edge of the cube be equal to x.

2. It is known from the problem statement that if each edge of the cube is increased by 3, then its total surface area will increase by 126.

3. It follows from the definition that the total surface area of ​​a cube is equal to the sum of the areas of all its faces. The area of ​​a cube face is equal to the square of the cube edge. Therefore, before increasing the edge of the cube, the total surface area was calculated as 6x² (since the cube has 6 edges). After increasing the rib by 3, the total surface area will be calculated as 6 (x + 3) ².

4. Let’s compose and solve the equation

6x² + 126 = 6 (x + 3) ²,

6x² + 126 = 6x² + 36x + 54,

6x² – 6x² + 36x = 126 – 54,

36x = 72,

x = 2.

Answer: the edge of the cube is 2.