(x^\frac{1}{2} +1)(x^\frac{1}{2} -1) (x^(1)/(2) +1)(x^(1)/(2) -1)

Question

(x^\frac{1}{2} +1)(x^\frac{1}{2} -1)

`(x^(1)/(2) +1)(x^(1)/(2) -1)`

Answer 1

x-1

Explanation:

To simplify the expression (x^(1/2) + 1)(x^(1/2) - 1), we can use the difference of squares formula, which states that a^2 - b^2 = (a + b)(a - b).

In this case, let's rewrite the expression as follows:

(x^(1/2) + 1)(x^(1/2) - 1) = [(x^(1/2))^2 - 1^2]

Using the difference of squares formula, we have:

[(x^(1/2))^2 - 1^2] = (x^(1/2) + 1)(x^(1/2) - 1)

Therefore, the simplified expression is x - 1.