Question

√x-0,09=0,9;√x²-1=1;√x²+5=2​

Answer 1

Решение:

1) В записи данного уравнения под корнем только х, иначе была бы запись √(x-0,09)=0,9, поэтому здесь и в следующих уравнениях ничего додумывать не будем:

√x-0,09=0,9

√х = 0.9 + 0,09

√х = 0.99

х = 0.99²

х = 0,9801

Ответ: 0,9801.

2) √x²-1 = 1

lxl - 1 = 1

lxl = 1+1

lxl = 2

x = ± 2

Ответ: - 2; 2.

3) √x² + 5 = 2

lxl + 5 = 2

lxl = 2 - 5

lxl = - 3

уравнение корней не имеет.

Answer 2

To solve these equations for x, you can follow these steps:

1. √x - 0.09 = 0.9

To isolate x, first add 0.09 to both sides of the equation:

√x - 0.09 + 0.09 = 0.9 + 0.09

√x = 0.99

Now, square both sides to eliminate the square root:

(√x)² = (0.99)²

x = 0.99²

x = 0.9801

2. √x² - 1 = 1

Square both sides to eliminate the square root:

(x²) - 1 = 1

Now, add 1 to both sides of the equation:

x² - 1 + 1 = 1 + 1

x² = 2

Now, take the square root of both sides:

√(x²) = √2

x = ±√2

So, x can be both √2 and -√2.

3. √x² + 5 = 2

First, subtract 5 from both sides of the equation:

√x² + 5 - 5 = 2 - 5

√x² = -3

This equation doesn't have a real solution because the square root of a real number is always non-negative, and -3 is negative. Therefore, there are no real solutions for this equation.

So, the solutions for the given equations are:

1. x = 0.9801
2. x = √2 and x = -√2
3. No real solutions for this equation.