plify $$ (5+\sqrt{5})(5-\sqrt{5}) $$

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UpStudy AI · Accepted Answer

To simplify the expression $$ (5+\sqrt{5})(5-\sqrt{5}) $$, we can use the difference of squares formula, which states that $$ (a+b)(a-b) = a^2 - b^2 $$.

In this case, let:
- $$ a = 5 $$
- $$ b = \sqrt{5} $$

Now, applying the difference of squares formula:

$$
(5+\sqrt{5})(5-\sqrt{5}) = 5^2 - (\sqrt{5})^2
$$

Calculating each term:

$$
5^2 = 25
$$
$$
(\sqrt{5})^2 = 5
$$

Now substituting these values back into the equation:

$$
(5+\sqrt{5})(5-\sqrt{5}) = 25 - 5 = 20
$$

Thus, the simplified result is:

$$
\boxed{20}
$$
The simplified result is 20.

plify \( (5+\sqrt{5})(5-\sqrt{5}) \)

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