Question

- a) x² – 9 = 0;6) x2 - 5 = 0;B) x2 - 64 = 0;r) x2 - 10 = 0.​

Answer 1

Ответ:

а) 3²=9 9-9=0 Х=3

б)5:2=2,5 х=2,5

в)64:2=32 х=32

г)10:2=5 х=5

Answer 2

Ответ:

1. x=3

2. 2,5 или 5/2

3. 32

4. 5

Answer 3

Let's solve each of the quadratic equations one by one:

a) x² – 9 = 0

To solve this equation, we can factor the expression:

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

Setting each factor equal to zero, we have:

x + 3 = 0 or x - 3 = 0

Solving these equations, we get:

x = -3 or x = 3

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

6. x² - 5 = 0

This equation does not factor easily, so we can solve it using the quadratic formula. The quadratic formula states that for an equation of the form ax² + bx + c = 0, the solutions can be found using the formula:

x = (-b ± √(b² - 4ac)) / (2a)

In this case, a = 1, b = 0, and c = -5. Plugging in these values, we get:

x = (0 ± √(0² - 4(1)(-5))) / (2(1)) x = (0 ± √(0 + 20)) / 2 x = (0 ± √20) / 2 x = ± √20 / 2 x = ± √(4 * 5) / 2 x = ± (2√5) / 2 x = ± √5

Therefore, the solutions to the equation x² - 5 = 0 are x = √5 and x = -√5.

B) x² - 64 = 0

This equation can be factored as a difference of squares:

(x + 8)(x - 8) = 0

Setting each factor equal to zero, we have:

x + 8 = 0 or x - 8 = 0

Solving these equations, we get:

x = -8 or x = 8

Therefore, the solutions to the equation x² - 64 = 0 are x = -8 and x = 8.

r) x² - 10 = 0

This equation does not factor easily, so we can use the quadratic formula. In this case, a = 1, b = 0, and c = -10. Applying the quadratic formula, we get:

x = (-b ± √(b² - 4ac)) / (2a) x = (0 ± √(0² - 4(1)(-10))) / (2(1)) x = (0 ± √(0 + 40)) / 2 x = (0 ± √40) / 2 x = ± √40 / 2 x = ± √(4 * 10) / 2 x = ± (2√10) / 2 x = ± √10

Therefore, the solutions to the equation x² - 10 = 0 are x = √10 and x = -√10.