Question

А) 5х2 – 10 = 0; б) х2 + 4х = 0; в) 3х2 + 7х + 2 = 0; г) х2 – 8х + 12 = 0; д) х2 + х + 3 = 0 е) (2х - 1)(2х + 1) – (х - 3)(х + 1) = 18. Срочно! Решите пожалуйста(

Answer 1

Solution:

a) To solve the equation 5x^2 - 10 = 0, we can start by adding 10 to both sides of the equation to isolate the term with x^2:

5x^2 - 10 + 10 = 0 + 10

Simplifying the equation gives us:

5x^2 = 10

Next, we can divide both sides of the equation by 5 to solve for x^2:

(5x^2)/5 = 10/5

Simplifying further, we get:

x^2 = 2

To find the value of x, we can take the square root of both sides of the equation:

√(x^2) = √2

Therefore, the solutions to the equation are:

x = ±√2

b) For the equation x^2 + 4x = 0, we can factor out x from the equation:

x(x + 4) = 0

This equation will be true if either x = 0 or x + 4 = 0. Solving for x gives us:

x = 0 or x = -4

c) To solve the equation 3x^2 + 7x + 2 = 0, we can factorize the equation:

(3x + 1)(x + 2) = 0

Setting each factor equal to zero, we get:

3x + 1 = 0 or x + 2 = 0

Solving for x gives us:

x = -1/3 or x = -2

d) For the equation x^2 - 8x + 12 = 0, we can factorize the equation:

(x - 2)(x - 6) = 0

Setting each factor equal to zero, we get:

x - 2 = 0 or x - 6 = 0

Solving for x gives us:

x = 2 or x = 6

e) To solve the equation (2x - 1)(2x + 1) - (x - 3)(x + 1) = 18, we can expand and simplify the equation:

(4x^2 - 1) - (x^2 - 9) = 18

Expanding the equation gives us:

4x^2 - 1 - x^2 + 9 = 18

Combining like terms, we get:

3x^2 + 8 = 18

Next, we can subtract 8 from both sides of the equation:

3x^2 = 10

Dividing both sides of the equation by 3 gives us:

x^2 = 10/3

To find the value of x, we can take the square root of both sides of the equation:

√(x^2) = √(10/3)

Therefore, the solutions to the equation are:

x = ±√(10/3)

Note: The solutions may be expressed as decimals or fractions depending on the desired level of precision.

I hope this helps! Let me know if you have any further questions.