Question

X⁴+x²-12=0 порешите мне

Answer 1

Все на фото) не хотела печатать))надеюсь все поймешь)

Answer 2

Solving the Equation x⁴ + x² - 12 = 0

To solve the equation x⁴ + x² - 12 = 0, we can use factoring or the quadratic formula. Let's go through both methods.

Method 1: Factoring

To factor the equation x⁴ + x² - 12 = 0, we can treat it as a quadratic equation in terms of x². Let's substitute y = x²:

y² + y - 12 = 0

Now we can factor this quadratic equation:

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

Setting each factor equal to zero, we have:

y + 4 = 0 or y - 3 = 0

Solving for y, we get:

y = -4 or y = 3

Substituting back y = x², we have:

x² = -4 or x² = 3

Taking the square root of both sides, we get:

x = ±2i or x = ±√3

Therefore, the solutions to the equation x⁴ + x² - 12 = 0 are x = ±2i and x = ±√3.

Method 2: Quadratic Formula

Alternatively, we can solve the equation x⁴ + x² - 12 = 0 using the quadratic formula. The quadratic formula states that for an equation of the form ax² + bx + c = 0, the solutions for x can be found using the formula:

x = (-b ± √(b² - 4ac)) / (2a)

In this case, a = 1, b = 1, and c = -12. Substituting these values into the quadratic formula, we have:

x = (-(1) ± √((1)² - 4(1)(-12))) / (2(1))

Simplifying further:

x = (-1 ± √(1 + 48)) / 2

x = (-1 ± √49) / 2

x = (-1 ± 7) / 2

This gives us two possible solutions:

x = (-1 + 7) / 2 = 6 / 2 = 3

x = (-1 - 7) / 2 = -8 / 2 = -4

Therefore, the solutions to the equation x⁴ + x² - 12 = 0 are x = 3 and x = -4.

Summary

The solutions to the equation x⁴ + x² - 12 = 0 are x = ±2i, x = ±√3, x = 3, and x = -4.