Question

4(х²-2)²-9(х²-2)+2=0​

Answer 1

Ответ и решение на фото:

Answer 2

To solve the quadratic equation 4(x² - 2)² - 9(x² - 2) + 2 = 0, you can use a substitution to simplify the equation and then solve for the variable x.

Let's make a substitution:

Let y = x² - 2. Now, we can rewrite the equation as:

4y² - 9y + 2 = 0

Now, we have a quadratic equation in terms of y. To solve it, you can use the quadratic formula:

y = (-b ± √(b² - 4ac)) / (2a)

In this case, a = 4, b = -9, and c = 2. Plug these values into the quadratic formula:

y = (-(-9) ± √((-9)² - 4(4)(2))) / (2(4))

Simplify:

y = (9 ± √(81 - 32)) / 8

y = (9 ± √49) / 8

y = (9 ± 7) / 8

Now, you have two possible values for y:

1. y = (9 + 7) / 8 = 16 / 8 = 2
2. y = (9 - 7) / 8 = 2 / 8 = 1/4

Remember that we made a substitution earlier: y = x² - 2. So, we need to solve for x:

For y = 2: x² - 2 = 2 x² = 2 + 2 x² = 4 x = ±√4 x = ±2

For y = 1/4: x² - 2 = 1/4 x² = 1/4 + 2 x² = 9/4 x = ±√(9/4) x = ±(3/2)

So, the solutions to the original equation 4(x² - 2)² - 9(x² - 2) + 2 = 0 are:

1. x = 2
2. x = -2
3. x = 3/2
4. x = -3/2