If x = (√3 - 2)/(√2 + 1), then which of the following equals to x - 4?

Question: If x = (√3 - 2)/(√2 + 1), then which of the following equals to x - 4?

সমাধান:
দেয়া আছে,
x = (√3 - 2)/(√2 + 1)
⇒ x = {(√3 - 2)(√2 - 1)}/{(√2 + 1)(√2 - 1)}
⇒ x = (√3 ⋅ √2 - √3 ⋅ 1 - 2 ⋅ √2 + 2 ⋅ 1)/{(√2)² - (1)²}
⇒ x = (√6 - √3 - 2√2 + 2)/(2 - 1)
⇒ x = √6 - √3 - 2√2 + 2
∴ x - 4 = √6 - √3 - 2√2 + 2 - 4
⇒ x - 4 = - 2√2 + √6 - √3 - 2

সঠিক উত্তর: (ক) - 2√2 + √6 - √3 - 2