Question

1)x-x^2=0 2)-3x^2+2x+1>0 3)(x^2-1)(x^2-5x+4)=0 4)x^2-4=0

Answer 1

Объяснение:

1)хе

2)хе(0.4)

3)хе

4)х=2

на картинке показано

Answer 2

Let's solve each of these equations and inequalities one by one:

1. x - x^2 = 0: To solve this equation, we can factor out an 'x' from both terms: x(1 - x) = 0

Now, we have two factors:

1. x = 0
2. 1 - x = 0

For the second factor, solve for x: 1 - x = 0 x = 1

So, the solutions to the equation are x = 0 and x = 1.

2. -3x^2 + 2x + 1 > 0: To solve this inequality, we can start by finding the roots of the corresponding equation, where the left side equals 0: -3x^2 + 2x + 1 = 0

We can solve this quadratic equation using the quadratic formula: x = (-b ± √(b^2 - 4ac)) / (2a)

In this case, a = -3, b = 2, and c = 1.

x = (-2 ± √(2^2 - 4(-3)(1))) / (2(-3)) x = (-2 ± √(4 + 12)) / (-6) x = (-2 ± √16) / (-6) x = (-2 ± 4) / (-6)

Now, we have two roots:

1. x = (-2 + 4) / (-6) = 2 / (-6) = -1/3
2. x = (-2 - 4) / (-6) = -6 / (-6) = 1

So, the roots are x = -1/3 and x = 1. Now, we need to determine the sign of the inequality in the intervals created by these roots.

-3x^2 + 2x + 1 > 0

In the interval (-∞, -1/3), the quadratic is positive since the coefficient of x^2 is negative, and it opens downwards. In the interval (-1/3, 1), the quadratic is negative. In the interval (1, ∞), the quadratic is positive.

So, the solution to the inequality is: x < -1/3 or x > 1

3. (x^2 - 1)(x^2 - 5x + 4) = 0: This is a quadratic equation with a factored form. Let's solve it:

First factor the equation: (x^2 - 1)(x^2 - 5x + 4) = 0

Now, we have two factors:

1. x^2 - 1 = 0
2. x^2 - 5x + 4 = 0

Solve each factor:

1. x^2 - 1 = 0 x^2 = 1 x = ±1

2. x^2 - 5x + 4 = 0 This quadratic equation can be factored further: (x - 4)(x - 1) = 0

Now, we have two factors: x - 4 = 0 x = 4

x - 1 = 0 x = 1

So, the solutions to the equation are x = ±1, x = 1, and x = 4.

4. x^2 - 4 = 0: To solve this equation, you can factor it: x^2 - 4 = (x - 2)(x + 2) = 0

Now, we have two factors:

1. x - 2 = 0 x = 2

2. x + 2 = 0 x = -2

So, the solutions to the equation are x = 2 and x = -2.