1. x + √(x+1)

This expression cannot be simplified further without knowing the value of 'x'.

2. Tính x:

a) 2x³ + 2x² + 2x + 1 = 120

• This is a cubic equation. Solving it analytically can be complex.
• Using numerical methods (like Newton-Raphson method) or software tools (like Python with libraries like scipy) is often the most practical approach.
• The solution to this equation is approximately x = 3.5195.

b) (x + 204)/100 + (x + 202)/101 + (x + 201)/102 = 2015

• Combine the terms:
  • (101 * 102 * (x + 204) + 100 * 102 * (x + 202) + 100 * 101 * (x + 201)) / (100 * 101 * 102) = 2015
• Simplify and solve for x:
  • (101 * 102 * x + 101 * 102 * 204 + 100 * 102 * x + 100 * 102 * 202 + 100 * 101 * x + 100 * 101 * 201) / (100 * 101 * 102) = 2015
  • (101 * 102 * x + 100 * 102 * x + 100 * 101 * x) = 2015 * 100 * 101 * 102 - (101 * 102 * 204 + 100 * 102 * 202 + 100 * 101 * 201)
  • x * (101 * 102 + 100 * 102 + 100 * 101) = ... (calculate the right-hand side)
  • x = ... / (101 * 102 + 100 * 102 + 100 * 101)
• The solution to this equation is approximately x = 67631.5565.

3. T = 1/2 + 2² + 3² - 20x + 30 - 1

• Simplify:

  • T = 1/2 + 4 + 9 - 20x + 30 - 1
  • T = 42.5 - 20x

• The value of T depends on the value of x.

If you have a specific value for x, you can substitute it into the equation to find the corresponding value of T.