Question

Решите уравнения (с объяснениями что и как) 1) x^2=6-x 2) x^2+4=-3 3) x^2-4x=0 4) x^3+2=3x

Answer 1

Ответ:

1) X^2=6-x . X^2-6+x=0 . X^2+x-6=0 . x=-1±√1^2 -4*1*(-6)÷2*1 . X= -1±√1+24÷2 .

X= -1±5÷2  x=2 X= -3

2) x^2+4=-3.  x^2= -3-4.  x^2= -7  x=±√-7

3) x^2-4x=0  x*(x-4)=0   x=0       x=0

                                      x-4=0    x=4

Объяснение:

Answer 2

1. x^2 = 6 - x:

To solve this equation, we can rearrange it into a quadratic form:

x^2 + x - 6 = 0

Now, we can factorize the quadratic equation:

(x + 3)(x - 2) = 0

To find the values of x, we set each factor equal to zero:

x + 3 = 0 --> x = -3 x - 2 = 0 --> x = 2

So the solutions to the equation are x = -3 and x = 2.

2. x^2 + 4 = -3:

To solve this equation, we can isolate x^2 by subtracting 4 from both sides:

x^2 = -7

Since the square of a real number cannot be negative, this equation has no real solutions. The solution would involve complex numbers, specifically imaginary numbers.

3. x^2 - 4x = 0:

To solve this equation, we can factor out x:

x(x - 4) = 0

Setting each factor equal to zero:

x = 0 or x - 4 = 0

Solving the second equation:

x - 4 = 0 --> x = 4

So the solutions to the equation are x = 0 and x = 4.

4. x^3 + 2 = 3x:

To solve this equation, we can rearrange it into a cubic form:

x^3 - 3x + 2 = 0

Unfortunately, there is no simple method to find the solutions to a cubic equation like this. One possible approach is to use numerical methods or calculators to approximate the solutions. In this case, the solutions are approximately x = -1.7693, x = 0.3846, and x = 2.3847.