Question

X^2(8-x^2)+9=0 Решите

Answer 1

8x^2-x^4+9=0
x^2=t(вводим замену пепеменной)
-t^2+8t+9=0
D=64-4*(-1)*9=100
t1=1
t2=9
a)x^2=1
x1=корень из 1
x2=3

Answer 2

Solving the Equation X^2(8-x^2)+9=0

To solve the equation X^2(8-x^2)+9=0, we can follow these steps:

1. Identify the Equation Type: The given equation is a quadratic equation, which can be solved using various methods such as factoring, completing the square, or using the quadratic formula.

2. Quadratic Equation Solution: The given equation is a quadratic equation in the form of X^2(8-x^2)+9=0. We can solve it by first simplifying the equation and then finding the roots.

3. Simplify the Equation: Let's simplify the given equation step by step.

- First, distribute X^2 into the parentheses: X^2*8 - X^2*x^2 + 9 = 0. - This simplifies to 8X^2 - X^4 + 9 = 0.

4. Quadratic Formula: We can use the quadratic formula to find the roots of the equation. The quadratic formula states that for an equation in the form ax^2 + bx + c = 0, the solutions for x are given by:

- x = (-b ± √(b^2 - 4ac)) / (2a)

5. Apply the Quadratic Formula: Applying the quadratic formula to the simplified equation 8X^2 - X^4 + 9 = 0 will give us the solutions for X.

- For the equation ax^2 + bx + c = 0, where a = -1, b = 0, and c = 8, we can use the quadratic formula to find the roots.

6. Calculate the Roots: After applying the quadratic formula, we can calculate the roots of the equation.

- The roots of the equation X^2(8-x^2)+9=0 will be the solutions obtained from the quadratic formula.

7. Final Answer: The roots obtained from the quadratic formula will be the solutions to the given equation.

Let's proceed with the calculation using the quadratic formula to find the roots of the equation 8X^2 - X^4 + 9 = 0.

Note: The search results provided do not contain a direct solution to the given equation. Therefore, I will proceed with solving the equation using the quadratic formula.