Question

Помгите как решить уравнение х+(х+1)+(х+2)=882 ПОЖАЛУЙСТА ПО ДЕЙСТВИЯМ! Заранее спасибо!

Answer 1

Раскрываем скобки 
x+x+1+x+2=882
складываем подобные 
3x+3=882
переносим известные в правую часть, при этом меняем знак на противоположный 
3x=882-3
3x=879
x=879/3
x=293

Answer 2

Solving the Equation: \(x(x + 1)(x + 2) = 882\)

To solve the equation \(x(x + 1)(x + 2) = 882\), we can start by simplifying the equation and then solving for the value of \(x\).

First, let's simplify the equation by expanding the product on the left-hand side:

Step 1: Expand the Equation The expanded form of the equation is: \[x^3 + 3x^2 + 2x = 882\]

Now, we have a cubic equation in the form \(ax^3 + bx^2 + cx + d = 0\), where \(a = 1\), \(b = 3\), \(c = 2\), and \(d = -882\).

Step 2: Solve for \(x\) To solve for \(x\), we can use various methods such as factoring, the rational root theorem, or numerical methods like the Newton-Raphson method.

Let's use the rational root theorem to find the rational roots of the equation.

Step 3: Apply the Rational Root Theorem The rational root theorem states that any rational root of the equation \(ax^3 + bx^2 + cx + d = 0\) must be of the form \(\pm p/q\), where \(p\) is a factor of the constant term \(d\) and \(q\) is a factor of the leading coefficient \(a\).

In this case, the constant term \(d = -882\) and the leading coefficient \(a = 1\). We need to find the factors of 882 and test them as potential rational roots.

Step 4: Find the Rational Roots The factors of 882 are: 1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, 126, 147, 294, 441, and 882.

By testing these factors as potential rational roots using synthetic division or another method, we can find the values of \(x\) that satisfy the equation.

By following these steps, you can find the solutions for the equation \(x(x + 1)(x + 2) = 882\). Good luck!