Question

Упростить: √( х - 2√( х - 1 ) ) - √( х + 2√( х - 1 ) )

Answer 1

I hope this helps you

Answer 2

To simplify the given expression, we'll take it step by step:

Let's denote √(x - 1) as a for simplicity.

So, the expression becomes:

√(x - 2a) - √(x + 2a)

To combine these square roots, we need to rationalize the denominators by multiplying each term by its conjugate:

[√(x - 2a) - √(x + 2a)] * [√(x - 2a) + √(x + 2a)] / [√(x - 2a) + √(x + 2a)]

The middle part, [√(x - 2a) - √(x + 2a)] * [√(x - 2a) + √(x + 2a)], will cancel out because it's the difference of squares.

We are left with:

(√(x - 2a) + √(x + 2a)) / [√(x - 2a) + √(x + 2a)]

Now, the common term in the numerator and denominator can be canceled out:

1

So, the simplified expression is:

1