Question

как решить?заранее спасибо!!!!при каком значении а сумма квадратов корней уравнения x^2+(1-а)х-2а=0 равна 9????

Answer 1

Система двух уравнений:
-(1-а)= х1+х2
-2а= х1•х2
Возведем первое уравнение в квадрат:
а^2-2а+1=х1^2+х2^2+2х1•х2
-2а=х1х2

Т к сумма квадратов корней равна 9, то подставляем число 9 и вместо произведения корней подставляем -2а
а^2-2а+1=9+2•(-2а)
а^2-2а+1= 9-4а
а^2+2а-8=0
Д= 4+32=36
а= -2+-6/2=-4; 2
Ответ при а=-4 и 2

Answer 2

Сумма корней равна (а-1)
произведение корней равно (-2а)
(х1+х2) в квадрате минус 2х1х2 равно 9
(а -1) в квадрате минус 2*(-2а) равно 9 
дальше решить квадратное уравнение и найти а

Answer 3

Solving the Equation x^2 + (1-а)x - 2а = 0

To find the value of 'a' when the sum of the squares of the roots of the equation x^2 + (1-а)x - 2а = 0 is equal to 9, we can use the following steps:

Step 1: Find the roots of the equation. Step 2: Calculate the sum of the squares of the roots. Step 3: Set the sum of the squares of the roots equal to 9 and solve for 'a'.

Let's go through each step in detail.

# Step 1: Finding the Roots of the Equation

To find the roots of the equation x^2 + (1-а)x - 2а = 0, we can use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

In this equation, a = 1, b = (1-а), and c = -2а.

Substituting the values into the quadratic formula, we get:

x = (-(1-а) ± √((1-а)^2 - 4(1)(-2а))) / (2(1))

Simplifying further:

x = (-1 + а ± √(1 - 2а + а^2 + 8а)) / 2

x = (-1 + а ± √(а^2 + 9а + 1)) / 2

# Step 2: Calculating the Sum of the Squares of the Roots

Let's denote the roots as x1 and x2. The sum of the squares of the roots can be calculated as:

Sum of Squares = x1^2 + x2^2

Substituting the values of x1 and x2, we get:

Sum of Squares = ((-1 + а)^2 + (а^2 + 9а + 1)^2) / 4

# Step 3: Setting the Sum of the Squares of the Roots Equal to 9

Now, we can set the sum of the squares of the roots equal to 9 and solve for 'a':

(((-1 + а)^2 + (а^2 + 9а + 1)^2) / 4) = 9

Simplifying the equation:

((-1 + а)^2 + (а^2 + 9а + 1)^2) = 36

Expanding and rearranging the equation:

2а^4 + 18а^3 + 2а^2 - 34а - 35 = 0

Unfortunately, at this point, the equation becomes quite complex and does not have a simple solution. It may require numerical methods or further simplification to find the exact value of 'a' that satisfies the equation.

Please note that the equation and its solution may vary depending on the specific context or constraints provided. If you have additional information or specific requirements, please let me know, and I'll be happy to assist you further.