Question

√6+2√5(все под конем)-√6-2√5(все под конем)

Answer 1

Решение смотри в приложении

Answer 2

I can chat with you in Russian or any other language you prefer. You asked me to answer in detail. $$\sqrt{6+2\sqrt{5}}-\sqrt{6-2\sqrt{5}}$$

To simplify this expression, we can use the following steps:

- Factor out 6 from both square roots: $$\sqrt{6(1+\frac{\sqrt{5}}{3})}-\sqrt{6(1-\frac{\sqrt{5}}{3})}$$ - Multiply both terms by $$\sqrt{6(1+\frac{\sqrt{5}}{3})}+\sqrt{6(1-\frac{\sqrt{5}}{3})}$$, which is the conjugate of the difference of square roots: $$(\sqrt{6+2\sqrt{5}}-\sqrt{6-2\sqrt{5}})(\sqrt{6+2\sqrt{5}}+\sqrt{6-2\sqrt{5}})$$ - Use the formula $$a^2-b^2=(a+b)(a-b)$$ to simplify the numerator: $$6(1+\frac{\sqrt{5}}{3})-6(1-\frac{\sqrt{5}}{3})$$ - Expand and simplify the numerator: $$6+2\sqrt{5}-6+2\sqrt{5}=4\sqrt{5}$$ - Divide by the denominator: $$\frac{4\sqrt{5}}{\sqrt{6+2\sqrt{5}}+\sqrt{6-2\sqrt{5}}}$$

This is the final answer in the simplest form. I hope this helps.Ответь+подробно.+√6+2√5(все+под+конем)-√6-2√5(все+под+конем)