Question

(x-1)(x+1)=2(5x-10 целых 1/2) решить дискриминантом

Answer 1

Solving the Equation and Finding the Discriminant

To solve the equation (x-1)(x+1) = 2(5x-10+1/2) and find the discriminant, we can start by expanding the equation and simplifying it.

Expanding the equation: (x-1)(x+1) = 2(5x-10+1/2) x^2 - 1 = 10x - 20 + 1

Simplifying the equation: x^2 - 1 = 10x - 19

Now, let's bring all the terms to one side of the equation to get a quadratic equation in standard form: x^2 - 10x + 19 - 1 = 0 x^2 - 10x + 18 = 0

To find the discriminant, we can use the formula: Discriminant (D) = b^2 - 4ac

In this case, the quadratic equation is in the form ax^2 + bx + c = 0, where: a = 1, b = -10, and c = 18.

Calculating the discriminant: D = (-10)^2 - 4(1)(18) D = 100 - 72 D = 28

The discriminant is 28.

Now, we can use the discriminant to determine the nature of the solutions of the quadratic equation.

If the discriminant is: - Greater than 0 (D > 0): The equation has two distinct real solutions. - Equal to 0 (D = 0): The equation has one real solution (a repeated root). - Less than 0 (D < 0): The equation has no real solutions (complex roots).

Since the discriminant D = 28 is greater than 0, the quadratic equation x^2 - 10x + 18 = 0 has two distinct real solutions.

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