Question

(√(√11-5) ²-√(3-√11) ²)=

Answer 1

Ответ:Сначала рассмотрим корни:

√(√11 - 5) = √(√11 - 5)

√(3 - √11) = √(3 - √11)

Теперь возведем их в квадраты:

(√(√11 - 5))² = (√11 - 5)

(√(3 - √11))² = (3 - √11)

Теперь вычитаем одно из другого:

(√(√11 - 5))² - (√(3 - √11))² = (√11 - 5) - (3 - √11)

Выполним операции с корнями и числами:

(√11 - 5) - (3 - √11) = √11 - 5 - 3 + √11

Сгруппируем подобные члены:

(2√11 - 8)

Итак, результат выражения (√(√11-5)² - √(3-√11)²) равен 2√11 - 8.

Answer 2

Ответ:

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Answer 3

Let's simplify the expression step by step:

1. Start with the given expression: √(√11 - 5)² - √(3 - √11)²

2. First, calculate the squares inside the square roots: (√11 - 5)² = (11 - 10√11 + 25) (3 - √11)² = (9 - 6√11 + 11)

3. Simplify the expressions inside the square roots: √(11 - 10√11 + 25) - √(9 - 6√11 + 11)

4. Combine like terms under each square root: √(36 - 10√11) - √(20 - 6√11)

5. Factor out the common factor of 2 from both expressions: 2√(18 - 5√11) - 2√(10 - 3√11)

6. Now, let's try to simplify further. Notice that 18 and 10 are both multiples of 2, so we can factor out 2 from the square roots: 2√(2 * (9 - 5√11)) - 2√(2 * (5 - 3√11))

7. Factor out 2 from both square roots: 2√2 * √(9 - 5√11) - 2√2 * √(5 - 3√11)

8. At this point, it's challenging to simplify further without numerical approximations. You can use a calculator to compute the approximate values of the expressions inside the square roots and then calculate the final result.

So, the expression (√(√11 - 5)² - √(3 - √11)²) simplifies to: 2√2 * √(9 - 5√11) - 2√2 * √(5 - 3√11)

To find the numerical value, you'll need to calculate the values inside the square roots and then subtract them as indicated.