Question

√3х-2=√2-3х ​

Answer 1

Ответ:

2/3.

Пошаговое объяснение:

√(3х-2)=√(2-3х)

ОДЗ:

{3х-2 ≥ 0,

{2-3х ≥ 0;

{х ≥ 2/3,

{х ≤ 2/3;

х = 2/3.

Покажем, что данное число является корнем :

√(3•2/3-2)=√(2-3•2/3)

√0 = √0

0 = 0 - верно.

Ответ: 2/3.

Answer 2

To solve the equation √3x - 2 = √2 - 3x, we need to isolate the variable x on one side of the equation. Here's the step-by-step solution:

Step 1: Get rid of square roots. Move both square roots to one side of the equation:

√3x - √2 = 2 - 3x

Step 2: Isolate the terms with x on one side and constants on the other side. Add 3x to both sides of the equation:

√3x + 3x - √2 = 2

Step 3: Combine the x terms. Factor out x from the left side:

x(√3 + 3) - √2 = 2

Step 4: Isolate x by moving the constant term to the other side. Add √2 to both sides of the equation:

x(√3 + 3) = 2 + √2

Step 5: Divide both sides by (√3 + 3) to solve for x:

x = (2 + √2)/(√3 + 3)

The expression (2 + √2)/(√3 + 3) is the final solution for the equation.