Question

Знайдіть добуток коренів рівняння (x-5)^4+(x-5)^2+2=0 Помогите пожалуйста

Answer 1

Ответ:

Нет решений

Объяснение:

Пусть у=(x-5)^2

y^2+y+2=0

Уравнение не имеет действительных решений, так как дискриминант  равен 1-8=-7 меньше 0

Answer 2

Finding the Product of the Roots of the Equation

To find the product of the roots of the given equation, we can use the Vieta's formulas. The Vieta's formulas state that for a quadratic equation of the form ax^2 + bx + c = 0, the product of the roots is c/a.

The given equation can be rewritten as: (x-5)^4 + (x-5)^2 + 2 = 0

By substituting (x-5)^2 as a variable, let's say u, the equation becomes: u^2 + u + 2 = 0

Now, we can use the Vieta's formulas to find the product of the roots.

The product of the roots of the equation u^2 + u + 2 = 0 is given by the constant term divided by the coefficient of u^2.

The constant term is 2, and the coefficient of u^2 is 1.

Therefore, the product of the roots of the equation u^2 + u + 2 = 0 is 2/1 = 2.

So, the product of the roots of the original equation (x-5)^4 + (x-5)^2 + 2 = 0 is also 2.