Question

Решить уравнение х^-6х-27=0 пользуясь теоремой виета. 2.упростить √25а+√36а-√49а.ребят срочно

Answer 1

1)x2-6x-27=0                        2)корень25а+корень36а+корень49а=
x1+x2=6                                   5а+6а+7а=18а 
x1*x2=-27
x1=-3
x2=9

Answer 2

Solving the equation using Vieta's theorem:

To solve the equation x^2 - 6x - 27 = 0 using Vieta's theorem, we can use the fact that the sum of the roots of a quadratic equation is equal to the negation of the coefficient of the linear term, and the product of the roots is equal to the constant term divided by the coefficient of the quadratic term.

In this case, the coefficient of the linear term is -6 and the constant term is -27. Therefore, the sum of the roots is 6 and the product of the roots is -27.

Let's denote the roots as r1 and r2. According to Vieta's theorem, we have the following equations:

r1 + r2 = 6 [[1]] r1 * r2 = -27 [[2]]

We can solve these equations to find the values of r1 and r2.

From equation [[1]], we can express r1 in terms of r2:

r1 = 6 - r2

Substituting this expression into equation [[2]], we get:

(6 - r2) * r2 = -27

Expanding and rearranging the equation, we have:

r2^2 - 6r2 + 27 = 0

Now we have a quadratic equation in terms of r2. We can solve this equation using the quadratic formula:

r2 = (-b ± √(b^2 - 4ac)) / (2a)

In this case, a = 1, b = -6, and c = 27. Substituting these values into the quadratic formula, we get:

r2 = (6 ± √((-6)^2 - 4(1)(27))) / (2(1))

Simplifying further:

r2 = (6 ± √(36 - 108)) / 2

r2 = (6 ± √(-72)) / 2

Since the discriminant is negative, the roots will be complex numbers. Let's simplify the expression under the square root:

√(-72) = √(72) * i = 6√2 * i

Therefore, the roots are:

r2 = (6 ± 6√2 * i) / 2

Simplifying:

r2 = 3 ± 3√2 * i

Now, we can find the value of r1 by substituting the value of r2 into the expression r1 = 6 - r2:

r1 = 6 - (3 ± 3√2 * i)

Simplifying:

r1 = 3 ∓ 3√2 * i

Therefore, the solutions to the equation x^2 - 6x - 27 = 0 are:

x = 3 + 3√2 * i and x = 3 - 3√2 * i.

Simplifying √25a + √36a - √49a:

To simplify the expression √25a + √36a - √49a, we can use the properties of square roots.

First, let's simplify each square root individually:

√25a = 5√a [[3]] √36a = 6√a [[4]] √49a = 7√a [[5]]

Now, we can substitute these simplified square roots back into the original expression:

√25a + √36a - √49a = 5√a + 6√a - 7√a

Combining like terms, we get:

√25a + √36a - √49a = (5 + 6 - 7)√a

Simplifying further:

√25a + √36a - √49a = 4√a

Therefore, the simplified expression is 4√a.

I hope this helps! Let me know if you have any further questions.