Question

Алгебра за 8 класс (х-2)^2+24=(2+3х)^2 4х^2+х - 5х-1 =х^2+17 _____ ___ _______ 3 6 9 через дискриминант

Answer 1

(x-2)^2+24=(2+3x)^2
x^2-4x+4+24=4+12x-9x^2=0
-8x^2-16x+24=0
a=-8,b=-16,c=24.
D=b^2-4ac.
D=256-4×(-8)×24=256+768=1024.
x1,2=(-b+-√D)÷2a=(16+-32)÷(-16).
x1=(16+32)÷(-16)=48÷(-16)=-3
x2=(16-32)÷(-16)=-16÷(-16)=1
Ответ: -3 и 1.

Answer 2

Solving the Equation Using the Discriminant

To solve the equation (x-2)^2 + 24 = (2+3x)^2 + 4x^2 + x - 5x - 1 = x^2 + 17, we can use the discriminant to find the roots of the equation.

The discriminant (Δ) of a quadratic equation in the form ax^2 + bx + c = 0 is given by the formula: Δ = b^2 - 4ac.

In this case, the equation is in the form ax^2 + bx + c = 0, where a = 1, b = -2, and c = 17.

Calculating the Discriminant

Using the formula, we can calculate the discriminant (Δ) as follows: Δ = (-2)^2 - 4*1*17 Δ = 4 - 68 Δ = -64

Analyzing the Discriminant

The discriminant (Δ) is -64. When the discriminant is negative, the quadratic equation has no real roots. Instead, it has two complex roots.

Conclusion

The equation x^2 + 17 has no real roots, but it has two complex roots. Therefore, the roots of the given equation can be found using the quadratic formula for complex numbers.

If you need further assistance with finding the complex roots using the quadratic formula, feel free to ask!