Question

решить уравнение:(Х²-5)²+4(Х²-5)+3=0я знаю, что здесь надо вроде через у выразитьмне ответ напишите хотя бы только

Answer 1

(Х²-5)²+4(Х²-5)+3=0

замена Х²-5=t

t^2+4t+3=0

t1=-1

t2=-3

x^2-5=-1

x^2=4

x1=2

x2=-2

x^2-5=-3

x^2=2

x3=sqrt(2)

x4=-sqrt(2)

Answer 2

Solving the Quadratic Equation

To solve the given equation (x² - 5)² + 4(x² - 5) + 3 = 0, we can use a substitution to simplify the equation. Let's substitute u = x² - 5. Then the equation becomes u² + 4u + 3 = 0.

Factoring the Quadratic Equation

We can factorize the quadratic equation u² + 4u + 3 = 0 to solve for u.

The factored form of the equation is: (u + 3)(u + 1) = 0.

Finding the Solutions

Now, we can solve for u by setting each factor equal to zero:

1. u + 3 = 0 gives us u = -3. 2. u + 1 = 0 gives us u = -1.

Substituting Back for x

Since we originally substituted u = x² - 5, we can now substitute back to find the solutions for x:

1. When u = -3, we have x² - 5 = -3. Solving for x gives us x = ±√2. 2. When u = -1, we have x² - 5 = -1. Solving for x gives us x = ±2.

So, the solutions to the original equation are: x = ±√2 and x = ±2.