Question

Сократить 5-√5/√10-5√2

Answer 1

Решение примера на фотографии.

Answer 2

To simplify the expression (5 - √5) / (√10 - 5√2), we can rationalize the denominator by multiplying both the numerator and the denominator by the conjugate of the denominator (√10 + 5√2):

(5 - √5) / (√10 - 5√2) * (√10 + 5√2) / (√10 + 5√2)

Now, we use the difference of squares formula (a^2 - b^2 = (a + b)(a - b)) to simplify the denominator:

[(5 - √5)(√10 + 5√2)] / [(√10)^2 - (5√2)^2] [(5 - √5)(√10 + 5√2)] / [10 - 50] [(5 - √5)(√10 + 5√2)] / [-40]

Next, distribute the numerator:

5√10 + 25√2 - √(5 * 10) - 5√(5 * 2) / -40 5√10 + 25√2 - √50 - 5√10 / -40 (5√10 - 5√10) + 25√2 - √50 / -40 25√2 - √50 / -40

Now, the expression is in its simplest form: (25√2 - √50) / -40.