Question

Решите (√3-1)²+2(√3-1)+5

Answer 1

$= 3 - 2 \sqrt{3} + 1 + 2 \sqrt{3} - 2 + 5 = 7$

Answer 2

To solve the expression (√3-1)² + 2(√3-1) + 5, follow these steps:

Step 1: Simplify the square of the first term (√3-1)²: (√3-1)² = (√3-1) * (√3-1) = (√3)² - 2√3 + 1 = 3 - 2√3 + 1 = 4 - 2√3.

Step 2: Distribute the 2 to each term inside the parentheses: 2(√3-1) = 2√3 - 2.

Now, the expression becomes: (√3-1)² + 2(√3-1) + 5 = (4 - 2√3) + (2√3 - 2) + 5

Step 3: Combine like terms: The -2√3 and +2√3 will cancel each other out. (4 - 2√3) + (2√3 - 2) + 5 = 4 + (-2√3 + 2√3) + (-2 + 5) = 4 + 0 + 3 = 7.

So, the simplified expression is 7.