Question

Решительно уравнения 1) √3x+1=x-3 2) √x-5=3

Answer 1

Второе кореньx=8; x=64

Answer 2

Let's first isolate the radical term on one side of the equation by subtracting x from both sides:

√3x + 1 - x = -3

Next, we can square both sides of the equation to eliminate the radical:

(√3x + 1 - x)^2 = (-3)^2

Expanding the left-hand side, we get:

3x + 1 - 2x√3x - 2√3x + x^2 + 2x - 1 = 9

Simplifying, we get:

x^2 - x√3x - √3x - 2x + 4 = 0

Now, we can factor the left-hand side:

(x - 4)(x + √3)(x - √3 - 1) = 0

Therefore, the solutions are:

x = 4, x = -√3, and x = √3 + 1

We can solve this equation by squaring both sides:

(x - 5)^2 = 3^2

Expanding the left-hand side, we get:

x^2 - 10x + 25 = 9

Subtracting 9 from both sides:

x^2 - 10x + 16 = 0

Now, we can factor the left-hand side:

(x - 2)(x - 8) = 0

Therefore, the solutions are:

x = 2 and x = 8

However, we need to check if these solutions satisfy the original equation.

For x = 2:

√2 - 5 = 3

This is not true, so x = 2 is not a solution.

For x = 8:

√8 - 5 = 3

This is true, so x = 8 is the only solution.

Therefore, the solution to the equation √x - 5 = 3 is x = 8.