Question

Срочнааааа !!!!СИЛ БОЛЬШЕ НЕТ , ВСЕ ПЕРЕПРОБЫВАЛА .ПЛИЗ ХЕЛП МИ ! решить уравнение (х+а)(х+2а)(х+3а)(х+4а)=360а^4 Ребят , только не из инета , не подходит .

Answer 1

$(x+a)(x+2a)(x+3a)(x+4a)=360a^4$

$[(x+a)(x+4a)]*[(x+2a)(x+3a)]=360a^4$

$[x^2+5ax+4a^2]*[x^2+5ax+6a^2]=360a^4$

пусть $t(x)=x^2+5ax$

$(t+4a^2)(t+6a^2)=360a^4$

$t^2+10a^2t+24a^4=360a^4$

$t^2+10a^2t-336a^4=0$

$t^2+24a^2t-14a^2t-336a^4=0$

$t(t+24a^2)-14a^2(t+24a^2)=0$

$(t-14a^2)(t+24a^2)=0$

$x^2+5ax-14a^2=0,or,x^2+5ax+24a^2=0$

дискриминант второго уравнения отрицателен, т.е. второе уравнение действительных корней не имеет: $D=(5a)^2-4*24a^2=25a^2-96a^2\ \textless \ 0$

первое же уравнение: 
$x^2+7ax-2ax-14a^2=0$

$x(x+7a)-2a(x-14a)=0$

$(x-2a)(x+7a)=0$

действительные корни уравнения: $x=2a,or,x=-7a$, ограничений на $a$ нету (все действительные числа)

Answer 2

[(x+a)(x+4a)]*[(x+2a)(x+3a)]=360a^4
(x²+5ax+4a²)(x²+5ax+6a²)=360a^4
x²+5ax+4a²=m
m(m+2a²)=360a^4
m²+2ma²-360a^4=0
m1+m2=-2a² U m1*m2=-360a^4
m1=-20a²⇒x²+5ax+4a²=-20a²
x²+5ax+24a²=0
D=25a²-96a²=-71a²<0 нет решения
m2=18a²⇒x²+5ax+4a²=18a²
x²+5ax-14a²=0
x1+x2=-5a U x1*x2=-14a
x1=-7a U x2=2a
Ответ x={-7a;2a},a∈R

Answer 3

Solving the Equation

To solve the given equation (x - a)(x + 2a)(x + 3a)(x + 4a) = 360a^4, we can start by expanding the equation and then simplifying it to find the values of x.

Expanding the equation: (x - a)(x + 2a)(x + 3a)(x + 4a) = 360a^4

Let's expand the equation and simplify it step by step.

Step 1: Expand the Equation

The expanded form of the given equation is: x^4 + 10ax^3 + 35a^2x^2 + 50a^3x + 24a^4 = 360a^4

Step 2: Simplify the Equation

Now, let's simplify the equation by rearranging the terms and setting it equal to zero: x^4 + 10ax^3 + 35a^2x^2 + 50a^3x + 24a^4 - 360a^4 = 0

Simplifying further: x^4 + 10ax^3 + 35a^2x^2 + 50a^3x - 336a^4 = 0

Step 3: Solve for x

To solve for x, we can use various methods such as factoring, the quadratic formula, or other algebraic techniques. Let's proceed with factoring the equation and solving for x.

Factoring the equation may involve finding rational roots or using other methods to simplify the equation and solve for x.

I'll proceed with factoring the equation and solving for x to find the values that satisfy the given equation.