Question

1)6х^2+3х+101=0 2)11Х^2-х-10=0 3)х^2+3х=4 4)х^2=4х-3

Answer 1

Ответ:

Объяснение: Уравнения решаем через дискриминант

Answer 2

Let's solve the given quadratic equations one by one:

1. 6x^2 + 3x + 101 = 0

To solve this equation, we can use the quadratic formula, which states that for an equation in the form ax^2 + bx + c = 0, the solutions for x can be found using:

x = (-b ± √(b^2 - 4ac)) / (2a)

For the given equation, a = 6, b = 3, and c = 101. Substituting these values into the quadratic formula, we have:

x = (-3 ± √(3^2 - 4 * 6 * 101)) / (2 * 6) x = (-3 ± √(9 - 2424)) / 12 x = (-3 ± √(-2415)) / 12

Since the value inside the square root is negative, the solutions will involve complex numbers. Let's calculate the approximate values using a calculator:

x ≈ (-3 + √(-2415)i) / 12 ≈ (-3 + 49.14i) / 12 ≈ -0.25 + 4.095i x ≈ (-3 - √(-2415)i) / 12 ≈ (-3 - 49.14i) / 12 ≈ -0.25 - 4.095i

So, the solutions to the equation are approximately x ≈ -0.25 + 4.095i and x ≈ -0.25 - 4.095i.

2. 11x^2 - x - 10 = 0

Using the quadratic formula with a = 11, b = -1, and c = -10, we have:

x = (-(-1) ± √((-1)^2 - 4 * 11 * (-10))) / (2 * 11) x = (1 ± √(1 + 440)) / 22 x = (1 ± √441) / 22 x = (1 ± 21) / 22

So, the solutions are:

x = (1 + 21) / 22 = 22 / 22 = 1 x = (1 - 21) / 22 = -20 / 22 ≈ -0.909

Therefore, the solutions to the equation are x = 1 and x ≈ -0.909.

3. x^2 + 3x = 4

To solve this equation, we can rearrange it to the standard quadratic form:

x^2 + 3x - 4 = 0

Now we can apply the quadratic formula:

x = (-3 ± √(3^2 - 4 * 1 * (-4))) / (2 * 1) x = (-3 ± √(9 + 16)) / 2 x = (-3 ± √25) / 2 x = (-3 ± 5) / 2

So, the solutions are:

x = (-3 + 5) / 2 = 2 / 2 = 1 x = (-3 - 5) / 2 = -8 / 2 = -4

Therefore, the solutions to the equation are x = 1 and x = -4.

4. x^2 = 4x - 3

Bringing all terms to one side, we have:

x^2 - 4x + 3 = 0

Applying the quadratic formula:

x = (4 ± √((-4)^2 - 4 *