Question

1/(х-√х^2 )-1/(х+√х^2)=√3

Answer 1

Решение задания приложено

Answer 2

Let's solve the given equation step by step. The equation is:

1 / (x - √x^2) - 1 / (x + √x^2) = √3

Step 1: Simplify the denominators √x^2 is the same as |x| (the absolute value of x), so the denominators can be simplified as follows:

1 / (x - |x|) - 1 / (x + |x|) = √3

Step 2: Find the common denominator

The common denominator for the two fractions on the left side is (x - |x|)(x + |x|), which is simply (x^2 - x^2), resulting in:

1 / (x - |x|) - 1 / (x + |x|) = (x + |x| - x + |x|) / (x^2 - x^2) = 2|x| / (x^2 - x^2)

Step 3: Simplify the expression

Since x^2 - x^2 = 0, we cannot directly divide by it. It means the expression is undefined for x ≠ 0.

Step 4: Solve for x = 0

When x = 0, the equation becomes:

1 / (0 - |0|) - 1 / (0 + |0|) = √3

Simplifying further:

1 / (0 - 0) - 1 / (0 + 0) = √3

1 / 0 - 1 / 0 = √3

Since dividing by zero is undefined, there is no solution for x = 0.

Therefore, there is no real value of x that satisfies the original equation 1 / (x - √x^2) - 1 / (x + √x^2) = √3.