Question

X⁴-x²-12=0 ....................​

Answer 1

Ответ:

X^4-x^2-12=0 пусть x^2=y y^2-y-12=0 по теореме Виета: y1+y2=1 y1*y2=-12 y1=-3 y2=4 x^2=4 x1=-2; x2=2 x^2=-3 x-не имеет корней ответ: -2; 2

Answer 2

To solve the equation x⁴ - x² - 12 = 0, you can use a substitution to simplify it. Let's make a substitution:

Let y = x².

Now, the equation becomes y² - y - 12 = 0. This is a quadratic equation in y, which is easier to solve.

You can factor this equation:

(y - 4)(y + 3) = 0

Now, you have two possible solutions for y:

1. y - 4 = 0, which gives y = 4.
2. y + 3 = 0, which gives y = -3.

Remember that we made a substitution earlier, where y = x². So, you need to find the corresponding values of x:

1. For y = 4: Take the square root of both sides: x² = 4 Now, take the square root of 4: x = ±2

2. For y = -3: There are no real solutions because the square root of a negative number is not real. So, this branch does not yield any real solutions.

Therefore, the real solutions to the equation x⁴ - x² - 12 = 0 are x = 2 and x = -2.