Question

√x2-4Х-1=2 x-√x+1=5 √х√2-х=2х х-1 =√-1 √2х-1

Answer 1

Пошаговое объяснение:

1)

$\sqrt{ {x}^{2} - 4x - 1 } = 2 \\ {x}^{2} - 4x - 1 = 4 \\ {x}^{2} - 4x - 5 = 0 \\ x1 = 5 \\ x2 = - 1$

2)

$x - \sqrt{x + 1} = 5 \\ \sqrt{x + 1} =x - 5 \\ x + 1 = {x }^{2} - 10x + 25 \\ x \geqslant 5 \\ \\ {x}^{2} - 11x + 24 = 0 \\ x1 = 8 \\ x2 = 3$

x2 - не подходит, так как < 5

$\sqrt{x} \sqrt{2 - x} = 2x \\ x(2 - x) = 4 {x}^{2} \\ 0 \leqslant x \leqslant 2 \\ \\2x - {x}^{2} = 4 {x}^{2} \\ 5 {x}^{2} - 2x = 0 \\ x(5x - 2) = 0 \\ x = 0 \\ x = 0.4$

Answer 2

Let's go through each equation one by one and solve them:

1. √(x^2 - 4x - 1) = 2x To solve this equation, we'll square both sides of the equation to eliminate the square root: (x^2 - 4x - 1) = (2x)^2 x^2 - 4x - 1 = 4x^2 3x^2 + 4x + 1 = 0

This quadratic equation can be factored: (3x + 1)(x + 1) = 0

Setting each factor to zero and solving for x: 3x + 1 = 0 --> 3x = -1 --> x = -1/3

x + 1 = 0 --> x = -1

Therefore, the solutions to the equation are x = -1/3 and x = -1.

2. x - √(x + 1) = 5 To solve this equation, we'll isolate the square root term and then square both sides: x - 5 = √(x + 1) (x - 5)^2 = (√(x + 1))^2 x^2 - 10x + 25 = x + 1 x^2 - 11x + 24 = 0

This quadratic equation can be factored: (x - 3)(x - 8) = 0

Setting each factor to zero and solving for x: x - 3 = 0 --> x = 3 x - 8 = 0 --> x = 8

Therefore, the solutions to the equation are x = 3 and x = 8.

3. √(x√2 - x) = 2x To solve this equation, we'll square both sides of the equation: (x√2 - x) = (2x)^2 x√2 - x = 4x^2 x(√2 - 1) = 4x^2 (√2 - 1)x = 4x^2

Since x ≠ 0, we can divide both sides by x: √2 - 1 = 4x

Solving for x: x = (√2 - 1) / 4

4. x - 1 = √(-1 √(2x - 1)) We have a square root of a negative number (√(-1)), which is not a real number. Therefore, there are no real solutions to this equation.

Please note that in equations 1, 2, and 3, the solutions I provided are real number solutions. However, there might be additional complex solutions depending on the context or the range of solutions you're considering.