Question

Уравнение 6х^2+х-2=0 имеет корни х1 и х2. Не решая уравнения, найдите (х1^2 +х2^2)^2. Помогите пожалуйста,8 класс.

Answer 1

6x² + x - 2 = 0
x1 = 1/2,  x2 = - 2/3
(x1^2 + x2^2)^2 = (1/4 + 4/9)^2 = (25/36)^2 = 625/1296

Answer 2

Finding the Value of (x1^2 + x2^2)^2 without Solving the Equation

To find the value of (x1^2 + x2^2)^2 without solving the equation 6x^2 + x - 2 = 0, we can use the following approach:

First, we need to find the sum of the roots (x1 and x2) and the product of the roots. Then, we can use these values to calculate (x1^2 + x2^2)^2 without explicitly solving for x1 and **x2.

The sum of the roots (x1 and x2) can be found using the formula: x1 + x2 = -b/a.

The product of the roots can be found using the formula: x1 * x2 = c/a.

Now, we can use these values to calculate (x1^2 + x2^2)^2: (x1^2 + x2^2)^2 = (x1^2 + 2*x1*x2 + x2^2)^2.

Substituting the values of x1 + x2 and x1 * x2 into the equation, we can calculate (x1^2 + x2^2)^2 without explicitly solving for x1 and x2.

Let's proceed with the calculations.