Question

5.41. Решите уравнение:1) х²-9=0; 3) х²-81=0;2) х²-0,04=0;4) у²-1/9=0​

Answer 1

Ответ:

Объяснение:

1)x=3 x=-3

2)x=0.2 x=-0.2

3)x=9 x=-9

4)y=1/3 y=-1/3

Answer 2

1. x² - 9 = 0

Factorizing the equation, we have:

(x - 3)(x + 3) = 0

Setting each factor equal to zero, we get:

x - 3 = 0 or x + 3 = 0

Solving for x in each equation, we have:

x = 3 or x = -3

Therefore, the solutions to the equation x² - 9 = 0 are x = 3 and x = -3.

2. x² - 0.04 = 0

First, let's convert the decimal to a fraction:

0.04 = 4/100 = 1/25

Now, we can rewrite the equation as:

x² - 1/25 = 0

To solve for x, we can take the square root of both sides:

√(x² - 1/25) = √0

x - 1/5 = 0 or x + 1/5 = 0

Solving for x in each equation, we have:

x = 1/5 or x = -1/5

Therefore, the solutions to the equation x² - 0.04 = 0 are x = 1/5 and x = -1/5.

3. x² - 81 = 0

This equation is a difference of squares. We can rewrite it as:

(x - 9)(x + 9) = 0

Setting each factor equal to zero, we get:

x - 9 = 0 or x + 9 = 0

Solving for x in each equation, we have:

x = 9 or x = -9

Therefore, the solutions to the equation x² - 81 = 0 are x = 9 and x = -9.

4. y² - 1/9 = 0

First, let's move the constant term to the other side:

y² = 1/9

To solve for y, we can take the square root of both sides:

√(y²) = √(1/9)

y = ±1/3

Therefore, the solutions to the equation y² - 1/9 = 0 are y = 1/3 and y = -1/3.