Question

Y2 (в кварате) + Y + D = 0 Y1-Y2=6 найти D (теорема виета)

Answer 1

Ответ:

Объяснение:

y²+y+d=0, где y₁-y₂=6

y₁+y₂=-b/a=-1/1=-1

y₁·y₂=c/a=d/1=d

Система уравнений:

y₁-y₂=6

y₁+y₂=-1

y₁-y₂-y₁-y₂=6+1

-2y₂=7

y₂=7/(-2)=-3,5

y₁-3,5=-1; y₁=-1+3,5=2,5

2,5·(-7/2)=d

d=5/2 ·(-7/2)=-35/4=-8 3/4=-8,75

Answer 2

Finding D using the Vieta's theorem

To find the value of D in the equation Y^2 + Y + D = 0, we can use Vieta's theorem. Vieta's theorem states that for a quadratic equation of the form ax^2 + bx + c = 0, the sum of the roots is equal to -b/a, and the product of the roots is equal to c/a.

In this case, the equation is Y^2 + Y + D = 0. Let's find the sum and product of the roots using Vieta's theorem.

Let the roots of the equation be Y1 and Y2.

According to Vieta's theorem: - The sum of the roots (Y1 + Y2) is equal to -b/a. - The product of the roots (Y1 * Y2) is equal to c/a.

In our equation, a = 1, b = 1, and c = D.

Therefore, the sum of the roots (Y1 + Y2) is equal to -1/1 = -1, and the product of the roots (Y1 * Y2) is equal to D/1 = D.

We are given that Y1 - Y2 = 6. Using this information, we can find the individual values of Y1 and Y2.

Let's solve for Y1 and Y2 using the given information:

Y1 - Y2 = 6

From this equation, we can express Y1 in terms of Y2:

Y1 = Y2 + 6

Now, let's substitute this expression for Y1 in the equation Y1 * Y2 = D:

(Y2 + 6) * Y2 = D

Expanding the equation, we get:

Y2^2 + 6Y2 = D

Now, we have two equations: 1. Y1 + Y2 = -1 2. Y2^2 + 6Y2 = D

We can solve these equations simultaneously to find the values of Y1, Y2, and D.

Please note that without a specific value for Y1 - Y2 or additional information, we cannot determine the exact values of Y1, Y2, and D. We can only express them in terms of each other.

Let me know if you need any further assistance!