Question

x(x+2)(x+3)(x+5)=72решить уравнение.не знаю какой класс но в 11 я не могу это решить)))помогите))если можно с объяснением.

Answer 1

x(x+2)(x+3)(x+5)=72
x(x+5)(x+2)(x+3)=72
(x^2+5x)(x^2+5x+6)=72
t=x^2+5x

t(t+6)=72
t^2+6t-72=0
t= -12  или t=6
x^2+5x=-12                                   x^2+5x=6
x^2+5x+12=0                                x^2+5x-6=0
D=25-48=-23<0                           x=1  или x=-6
действительных корней нет 

Ответ: 1 и -6 

Answer 2

Solving the Equation x(x+2)(x+3)(x+5) = 72

To solve the equation x(x+2)(x+3)(x+5) = 72, we need to find the values of x that satisfy the equation. Let's break down the steps to solve it:

Step 1: Expand the equation - Expand the equation by multiplying the terms: x(x+2)(x+3)(x+5) = 72 x(x^2 + 5x + 6)(x+5) = 72 x(x^3 + 5x^2 + 6x + 5x^2 + 25x + 30) = 72 x(x^3 + 10x^2 + 31x + 30) = 72 x^4 + 10x^3 + 31x^2 + 30x = 72

Step 2: Rearrange the equation - Move all the terms to one side of the equation to set it equal to zero: x^4 + 10x^3 + 31x^2 + 30x - 72 = 0

Step 3: Factor the equation - Factoring a quartic equation can be complex and may require advanced techniques. In this case, we can use numerical methods or a graphing calculator to find the solutions.

Since you mentioned that you are unable to solve this equation, I recommend using a graphing calculator or numerical methods to find the approximate solutions. These methods can provide accurate solutions without the need for complex factoring techniques.

If you have access to a graphing calculator, you can graph the equation y = x^4 + 10x^3 + 31x^2 + 30x - 72 and find the x-values where the graph intersects the x-axis. These x-values will be the solutions to the equation.

Alternatively, you can use numerical methods such as the Newton-Raphson method or the bisection method to approximate the solutions. These methods involve iterative calculations to find the roots of the equation.

I hope this explanation helps you understand how to approach solving the equation x(x+2)(x+3)(x+5) = 72. If you have any further questions, please let me know!