Question

Sqrt4(21-10x)=12-sqrt4(21-10x)Люди добрые, объясните как решаеть, плз.

Answer 1

$\sqrt[4]{21-10x}=12-\sqrt[4]{21-10x}$

ОДЗ:
21-10x>0
10x<21
x<2.1

$\sqrt[4]{21-10x}=12-\sqrt[4]{21-10x}\\2\sqrt[4]{21-10x}=12\\\sqrt[4]{21-10x}=6\\(\sqrt[4]{21-10x})^4=6^4\\|21-10x|=1296\\21-10x=1296\ \ \ ili\ \ \ 21-10x=-1296\\10x=-1275\ \ \ \ \ \ \ ili\ \ \ 10x=1317\\x=-127.5\ \ \ \ \ \ \ \ \ ili\ \ \ x=131.7$
x=131.7 не входит в область допустимых задач.

Ответ: x=-127.5

Answer 2

Solving the Equation Sqrt4(21-10x) = 12 - sqrt4(21-10x)

To solve the equation Sqrt4(21-10x) = 12 - sqrt4(21-10x), we can follow these steps:

1. Let's start by simplifying the equation.

2. We'll first simplify the expressions inside the square roots.

3. Then, we'll isolate one of the square roots on one side of the equation and square both sides to solve for the variable.

Step 1: Simplify the Equation

The given equation is Sqrt4(21-10x) = 12 - sqrt4(21-10x).

Step 2: Simplify the Expressions Inside the Square Roots

We have Sqrt4(21-10x) and sqrt4(21-10x).

From the search results, we can see that sqrt4 is equivalent to 2. Therefore, Sqrt4(21-10x) simplifies to 2 * sqrt(21-10x).

Step 3: Isolate and Solve

Now, we can rewrite the equation as 2 * sqrt(21-10x) = 12 - 2 * sqrt(21-10x).

Let's isolate one of the square roots, for example, 2 * sqrt(21-10x), on one side of the equation:

2 * sqrt(21-10x) + 2 * sqrt(21-10x) = 12

4 * sqrt(21-10x) = 12

Now, we can solve for sqrt(21-10x):

sqrt(21-10x) = 12 / 4

sqrt(21-10x) = 3

Squaring both sides to solve for x:

(21-10x) = 3^2

(21-10x) = 9

Now, we can solve for x:

-10x = 9 - 21

-10x = -12

x = -12 / -10

x = 6 / 5

So, the solution to the equation Sqrt4(21-10x) = 12 - sqrt4(21-10x) is x = 6/5.