If the edge of the cube is reduced by 3 cm, then its volume will decrease by 189 cm3. What is the edge of a cube?

Let’s denote by x the initial length of the edge of the cube. The length of the edge of the cube after decreasing x is 3 cm. Let’s compose and solve the equation, considering that the volume of the cube has decreased by 189 cm3.

x ^ 3 – (x – 3) ^ 3 = 189.

x ^ 3 – (x ^ 3 – 3 * x ^ 2 * 3 + 3 * x * 3 ^ 2 – 3 ^ 3) = 189.

x ^ 3 – x ^ 3 + 9x ^ 2 – 27x – 27 = 189.

9x ^ 2 – 27x – 27 – 189 = 0.

9x ^ 2 – 27x – 162 = 0 | :nine.

x ^ 2 – 3x – 18 = 0.

According to Vieta’s theorem:

x1 + x2 = -p, where p = -3.

x1 * x2 = q, where q = -18.

The roots of the equation are equal: x1 = 6, x2 = -3 (does not fit).

Answer: The length of the edge of the cube is 6 cm.