Question

Алгебра срочно!!! Даю 70 баллов!!! 4sin^2x-3=0 По возможности решить двумя способами

Answer 1

Ответ:

4sinA2x - 3ÿ0

sin"2x:3/4

sinx::E V(3/4)

sinx:tn/3 /2

I)sinx:V3 /2

x:(-1)"n *arcsin(V3 /2)spin ,n:z

xz(-1)"n *pi/3+pin ,nzz

2)sinx:-V3 /2

x:(-1)"(n+l) *arcsin(V3 /2)spin ,n:z

xz(-1)"(n+l) *pi/3+pin ,nzz

Answer 2

Problem Statement

You have given the equation 4sin^2(x) - 3 = 0 and you need to solve it using two different methods.

Method 1: Factoring

To solve the equation 4sin^2(x) - 3 = 0 by factoring, we can rearrange the equation as follows:

4sin^2(x) = 3

Dividing both sides of the equation by 4, we get:

sin^2(x) = 3/4

Taking the square root of both sides, we have:

sin(x) = ±√(3/4)

Now, we need to find the values of x that satisfy this equation. Since sin(x) can take values between -1 and 1, we can rewrite the equation as:

x = arcsin(±√(3/4))

Using a calculator, we can find the values of x that satisfy this equation. The solutions will be in the form of x = arcsin(value).

Method 2: Quadratic Formula

To solve the equation 4sin^2(x) - 3 = 0 using the quadratic formula, we can rearrange the equation as follows:

4sin^2(x) = 3

Dividing both sides of the equation by 4, we get:

sin^2(x) = 3/4

Taking the square root of both sides, we have:

sin(x) = ±√(3/4)

Now, we can use the quadratic formula to find the values of x that satisfy this equation. The quadratic formula is given by:

x = (-b ± √(b^2 - 4ac)) / (2a)

In this case, a = 1, b = 0, and c = -3/4. Substituting these values into the quadratic formula, we get:

x = (0 ± √(0^2 - 4(1)(-3/4))) / (2(1))

Simplifying further, we have:

x = ± √(3/4) / 2

Now, we can find the values of x that satisfy this equation. The solutions will be in the form of x = ± √(3/4) / 2.

Please note that the exact values of x will depend on the specific values of √(3/4) and can be calculated using a calculator.

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