a) To solve for x, we need to isolate x on one side of the equation.

Given: x^3 - 5^2.2 + 31231 = 31245

We can simplify the equation by calculating 5^2.2:

x^3 - 25.2 + 31231 = 31245

x^3 - 50 + 31231 = 31245

x^3 + 31181 = 31245

Now, subtract 31181 from both sides:

x^3 = 31245 - 31181

x^3 = 64

To find x, we can take the cube root of both sides:

x = ∛64

x = 4

Therefore, x = 4.

b) The equation provided is incomplete. Please provide the complete equation.

c) The equation provided is incomplete. Please provide the complete equation.

d) To solve for x, we need to isolate x on one side of the equation.

Given: 3x^10 = 51 : 17.1024

We can simplify the equation by calculating 51 : 17.1024:

3x^10 = 2.976

Now, divide both sides by 3:

x^10 = 0.992

To find x, we can take the 10th root of both sides:

x = ∛∛∛∛∛∛∛∛∛0.992

x ≈ 0.992

Therefore, x ≈ 0.992.

e) To solve for x, we need to expand the equation and then isolate x on one side.

Given: (3x - 2)^3 = 2.32

Expanding the equation:

27x^3 - 54x^2 + 36x - 8 = 2.32

Now, subtract 2.32 from both sides:

27x^3 - 54x^2 + 36x - 10.32 = 0

There is no simple way to solve this equation algebraically. You may need to use numerical methods or a graphing calculator to find the approximate solutions.