Question

X=3x, 2x=1/2x+2, 3x=3x+4, x^2=9, x^2=1/16, x^2=6-x0, x^2+4x=-3, x^2-4x=0, x^3+2=3x

Answer 1

Смотри решение на фото

Answer 2

Let's solve each equation step by step:

1. X = 3x This equation is straightforward. To solve for x, we'll isolate it on one side: X = 3x Divide both sides by 3: x = X/3

2. 2x = 1/2x + 2 To solve for x, we'll first get rid of the fraction: Multiply both sides by 2 to eliminate the fraction: 4x = 1x + 4 Now, isolate x on one side: 4x - x = 4 3x = 4 Finally, divide by 3 to find the value of x: x = 4/3

3. 3x = 3x + 4 This equation seems to be incorrect. It states that the same value (3x) is equal to itself plus 4. This means there is no valid solution for x. The equation is inconsistent.

4. x^2 = 9 To solve for x, we need to take the square root of both sides (remembering to consider both the positive and negative square root): x = ±√9 x = ±3

5. x^2 = 1/16 Similarly, take the square root of both sides: x = ±√(1/16) x = ±(1/4) So, the two solutions are x = 1/4 and x = -1/4.

6. x^2 = 6 - x To solve this quadratic equation, we'll move all terms to one side and set it to zero: x^2 + x - 6 = 0 Now, we can factor or use the quadratic formula to find the solutions. Factoring: (x + 3)(x - 2) = 0 Setting each factor to zero: x + 3 = 0 or x - 2 = 0 x = -3 or x = 2

7. x^2 + 4x = -3 Move the constant to the other side: x^2 + 4x + 3 = 0 Now, we can factor it: (x + 3)(x + 1) = 0 Setting each factor to zero: x + 3 = 0 or x + 1 = 0 x = -3 or x = -1

8. x^2 - 4x = 0 Factor out x: x(x - 4) = 0 Setting each factor to zero: x = 0 or x - 4 = 0 x = 0 or x = 4

9. x^3 + 2 = 3x Move 3x to the other side: x^3 - 3x + 2 = 0 This equation is a cubic equation. Solving it exactly can be challenging, but we can observe that x = 1 is one of its roots (x^3 - 3x + 2 = 1 - 3 + 2 = 0). Now, we can factor the cubic polynomial using synthetic division: (x - 1)(x^2 + x - 2) = 0 Now, solve the quadratic factor: x^2 + x - 2 = 0 This quadratic can be factored: (x + 2)(x - 1) = 0 Setting each factor to zero: x + 2 = 0 or x - 1 = 0 x = -2 or x = 1

So, the solutions to each equation are as follows:

1. x = X/3
2. x = 4/3
3. No valid solution (inconsistent equation)
4. x = ±3
5. x = 1/4 or x = -1/4
6. x = -3 or x = 2
7. x = -3 or x = -1
8. x = 0 or x = 4
9. x = -2 or x = 1