Question

(5x+2)^3-25x (5x^3-4)=150x^2+21​

Answer 1

1)125х^3+150х^2+60х+8-25х=125х^3+150х^2+35х+8

2)подозреваю, что во втором примере ты забыл показатель

150х^2+21-5х^3+4=150х^2-5х^3+25

Answer 2

Let's solve the equation step by step:

Given equation: (5x+2)^3 - 25x(5x^3 - 4) = 150x^2 + 21

Step 1: Expand the left side of the equation using the binomial theorem for (5x+2)^3: (5x+2)^3 = (5x+2)(5x+2)(5x+2) = (25x^2 + 20x + 4)(5x+2) = 25x^3 + 10x^2 + 50x^2 + 20x + 10x + 4 = 25x^3 + 60x^2 + 30x + 4

Step 2: Distribute -25x to (5x^3 - 4): -25x(5x^3 - 4) = -25x * 5x^3 + (-25x) * (-4) = -125x^4 + 100x

Now our equation becomes: 25x^3 + 60x^2 + 30x + 4 - 125x^4 + 100x = 150x^2 + 21

Step 3: Move all terms to one side of the equation: -125x^4 + 25x^3 + 60x^2 + 30x + 4 - 150x^2 - 100x - 21 = 0

Step 4: Combine like terms: -125x^4 + 25x^3 - 90x^2 - 70x - 17 = 0

This is a fourth-degree polynomial equation. Solving fourth-degree equations generally involves factoring or using numerical methods. Factoring a fourth-degree polynomial is quite complex and often not feasible for general cases.

If you need to find specific solutions for this equation, you can use numerical methods such as graphing or iterative methods like Newton's method. Alternatively, you can use software or calculators that can handle complex equations to find approximate solutions for x.