Question

√(√3-2)²-³√(1-√3)³ обчистить

Answer 1

√(√3-2)²-³√(1-√3)³ = |√3 - 2| - (1 - √3) = 2 - √3 - 1 + √3 = 1

√3 < 2

|√3 - 2| = 2 - √3 модуль всегда положителен

Answer 2

To simplify the given expression, let's take it step by step:

1. (√3 - 2)²: (√3 - 2)² = (√3 - 2) × (√3 - 2) = (√3 - 2) × (√3 - 2) = (√3)² - 2 × √3 × 2 + 2² = 3 - 2√3 × 2 + 4 = 3 - 4√3 + 4 = 7 - 4√3

2. ³√(1 - √3)³: ³√(1 - √3)³ = (1 - √3)³ = 1³ - 3 × 1² × √3 + 3 × 1 × (√3)² - (√3)³ = 1 - 3√3 + 3√3² - √3³ = 1 - 3√3 + 3(√3)² - √3³ = 1 - 3√3 + 3(√3)² - √3 × √3² = 1 - 3√3 + 3(√3)² - √3 × 3 = 1 - 3√3 + 3(√3)² - 3√3 = 1 - 6√3 + 3(√3)² = 1 - 6√3 + 3 × 3 = 1 - 6√3 + 9 = 10 - 6√3

Now, the simplified expression is:

(√3 - 2)² - ³√(1 - √3)³ = (7 - 4√3) - (10 - 6√3)

Now, we can combine like terms:

= 7 - 4√3 - 10 + 6√3

Now, let's combine the constants and the square root terms separately:

= (7 - 10) + (-4√3 + 6√3)

= -3 + 2√3

So, the simplified expression is -3 + 2√3.