Question

(2x-1)(2x+1)-x(1-x)=2x(x+1)​

Answer 1

Ответ:

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Answer 2

To solve the given equation, let's simplify both sides step by step:

Starting with the left-hand side (LHS):

(LHS) = (2x - 1)(2x + 1) - x(1 - x)

Using the distributive property:

(LHS) = (4x^2 - 1) - x(1 - x)

Expanding further:

(LHS) = 4x^2 - 1 - (x - x^2)

Simplifying the negative sign:

(LHS) = 4x^2 - 1 - x + x^2

Rearranging the terms:

(LHS) = 4x^2 + x^2 - x - 1

Combining like terms:

(LHS) = 5x^2 - x - 1

Now, let's simplify the right-hand side (RHS):

(RHS) = 2x(x + 1)

Expanding:

(RHS) = 2x^2 + 2x

Now that we have simplified both sides, we can set them equal to each other:

5x^2 - x - 1 = 2x^2 + 2x

To solve this quadratic equation, let's move all terms to one side:

5x^2 - 2x^2 - x - 2x - 1 = 0

Combining like terms:

3x^2 - 3x - 1 = 0

Unfortunately, this quadratic equation does not factor easily. To find the solutions, we can use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

For our equation, a = 3, b = -3, and c = -1. Substituting these values into the quadratic formula:

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

Simplifying:

x = (3 ± √(9 + 12)) / 6

x = (3 ± √21) / 6

So the solutions to the equation are:

x = (3 + √21) / 6 x = (3 - √21) / 6

These are the two possible values of x that satisfy the given equation.