Question

(3-√2)(5+√2)-(√2-1)²

Answer 1

(3-√2)(5+√2)-(√2-1)²
15+3√2-5√2-2-(2-2√2+1)
15+3√2-5√2-2-(3-2√2)
15+3√2-5√2-2-3+2√2
10+0=10
Ответ:10

Answer 2

15+3√2-5√2-2-(2-2√2+1)
15+3√2-5√2-2-3+2√2
10

Answer 3

Let's simplify the expression step by step:

1. Expand the squared term: (√2 - 1)² = (√2 - 1)(√2 - 1) = 2 - 2√2 + 1 = 3 - 2√2.

2. Now the expression becomes: (3 - √2)(5 + √2) - (3 - 2√2).

3. Next, distribute the terms: (3)(5) + (3)(√2) - (√2)(5) - (√2)(√2) - (3) + (2√2).

4. Simplify the terms: 15 + 3√2 - 5√2 - 2 - 3 + 2√2.

5. Combine like terms: 15 + 2√2 - 2 - 3 = 10 + 2√2.

So, the final simplified expression is: 10 + 2√2.