Question

Решение задач с помощью евадратнвх уравнений

Answer 1

Есть несколько видов решение
ax^2+bx+c
D=b^2-4ac
(a-b)^2= (a-b)(a+b)
(a+b)^2= a^2+2ab-b^2

Answer 2

Solving Problems Using Quadratic Equations

Quadratic equations are equations of the form ax^2 + bx + c = 0, where a, b, and c are constants and x is the variable. These equations can be solved using various methods, such as factoring, completing the square, or using the quadratic formula.

Quadratic Formula

The quadratic formula is a widely used method for solving quadratic equations. It states that for the equation ax^2 + bx + c = 0, the solutions for x are given by: x = (-b ± √(b^2 - 4ac)) / (2a)

Example of Solving a Quadratic Equation

Let's consider the quadratic equation 3x^2 + 10x + 7 = 0. We can use the quadratic formula to find the solutions for x.

First, we identify the values of a, b, and c: - a = 3 - b = 10 - c = 7

Now, we can apply the quadratic formula to find the solutions for x: x = (-b ± √(b^2 - 4ac)) / (2a)

Substitute the values of a, b, and c into the formula: x = (-10 ± √(10^2 - 4*3*7)) / (2*3) x = (-10 ± √(100 - 84)) / 6 x = (-10 ± √16) / 6 x = (-10 ± 4) / 6

So, the solutions for x are: x1 = (-10 + 4) / 6 = -6 / 6 = -1 x2 = (-10 - 4) / 6 = -14 / 6 = -7/3

Therefore, the solutions for the given quadratic equation are x = -1 and x = -7/3.

This example demonstrates how the quadratic formula can be used to solve quadratic equations and find the values of the variable x.