Question

Решите уравнение. 4x^4-36x^2=0

Answer 1

$4x^4-36x^2=0\\4x^2(x^2-9)=0\;\;\;\;|:4\\x^2(x^2-9)=0\\x^2=0-->x=0\\x^2-9=0-->x=-3-->x=3\\x_{1}=-3 \\x_{2}=0 \\x_{3} =3$

Answer 2

4х⁴-36х²=0; вынесем за скобки 4х²

4х²(х²-9)=0  произведение равно 0, когда

один из сомножителей = 0

Если   х²=0;  то    х1=х2=0

Если х²-9=(х-3)(х+3)=0; то х-3=0;    х3=3;

или х+3=0;   х4=-3

Ответ: два одинаковых корня =0; -3; 3.

Уравнение 4-ой степени и корней четыре))

Answer 3

To solve the equation 4x^4 - 36x^2 = 0, we can factor out the common term x^2:

4x^4 - 36x^2 = 0

Factor out x^2:

x^2(4x^2 - 36) = 0

Now, we have a quadratic equation in the parentheses:

4x^2 - 36 = 0

Now, let's solve the quadratic equation for x^2:

4x^2 - 36 = 0

Add 36 to both sides:

4x^2 = 36

Divide both sides by 4:

x^2 = 9

Now, take the square root of both sides:

x = ±√9

x = ±3

So, the solutions to the original equation are x = 3 and x = -3.