Question

Решите уравнение: |x^2-4x-1|=x^2+6x+1

Answer 1

Думаю, что примерно так. решаю по типу ЕГЭшноного задания. рано или поздно придется понять))

Answer 2

I can help you solve the equation.

To solve the equation, we need to consider two cases: when the absolute value is positive and when it is negative.

Case 1: |x^2-4x-1| = x^2-4x-1

In this case, we can simplify the equation by subtracting x^2 from both sides:

-4x-1 = 6x+1

Then, we can solve for x by adding 4x and subtracting 1 from both sides:

-2 = 10x

Finally, we can divide both sides by 10 to get x:

x = -0.2

Case 2: |x^2-4x-1| = -(x^2-4x-1)

In this case, we can simplify the equation by multiplying both sides by -1:

x^2-4x-1 = -x^2+4x+1

Then, we can solve for x by adding x^2 and subtracting 4x from both sides:

2x^2-8x-2 = 0

Finally, we can use the quadratic formula to find the values of x:

x = \frac{8 \pm \sqrt{64+16}}{4}

x = \frac{8 \pm \sqrt{80}}{4}

x = \frac{8 \pm 4\sqrt{5}}{4}

x = 2 \pm \sqrt{5}

Therefore, the solutions of the equation are x = -0.2, x = 2 + \sqrt{5}, and x = 2 - \sqrt{5}.

You can check your answers by plugging them into the original equation and verifying that they satisfy it.

For more information on how to solve equations with absolute values, you can visit [this website](https://ru.symbolab.com/solver/equation-calculator).

I hope this helps. Have a nice day!