Question

1/(5-√27)+ 1/(√27+5)

Answer 1

Ответ:

-5

Объяснение:

1/(5-√27)+ 1/(√27+5) = (5+√27)/((5-√27)(5+√27)) + (5-√27)/((5-√27)(5+√27))=

= (5+√27 +5-√27)/(5²-(√27)²) = 10/(25-27) = 10/(-2) = -5

Answer 2

To simplify the expression, let's rationalize the denominators.

We have the expression:

1/(5 - √27) + 1/(√27 + 5)

First, let's rationalize the denominator of the first fraction, 1/(5 - √27):

To rationalize the denominator, we multiply the numerator and denominator by the conjugate of the denominator, which is (5 + √27):

[1/(5 - √27)] * [(5 + √27)/(5 + √27)]

Expanding this expression, we get:

(5 + √27)/(25 - 27)

Simplifying further:

(5 + √27)/(-2)

Now let's rationalize the denominator of the second fraction, 1/(√27 + 5):

To rationalize the denominator, we multiply the numerator and denominator by the conjugate of the denominator, which is (√27 - 5):

[1/(√27 + 5)] * [(√27 - 5)/(√27 - 5)]

Expanding this expression, we get:

(√27 - 5)/(27 - 25)

Simplifying further:

(√27 - 5)/2

Now we can combine the two fractions:

[(5 + √27)/(-2)] + [(√27 - 5)/2]

To add these fractions, we need to find a common denominator, which is 2:

[(5 + √27) + (√27 - 5)]/2

Simplifying the numerator:

(5 + √27 + √27 - 5)/2

Combining like terms:

(2√27)/2

Simplifying further:

√27

Since √27 is equal to 3√3, the final simplified expression is:

3√3