If x = (√3 - 2)/(√2 + 1), then which of the following equals to x - 4?
Solution
Correct Answer: Option A
Given,
x = (√3 - 2)/(√2 + 1)
= {(√3 - 2)(√2 - 1)}/{(√2 + 1)(√2 - 1)}
= (√3.√2 - 2√2 - √3 + 2)/{(√2)² - (1)²}
= (√6 - 2√2 - √3 + 2)/1
= √6 - 2√2 - √3 + 2
∴ x - 4 = √6 - 2√2 - √3 + 2 - 4
= √6 - 2√2 - √3 - 2
= -2√2 + √6 - √3 - 2
x = (√3 - 2)/(√2 + 1)
= {(√3 - 2)(√2 - 1)}/{(√2 + 1)(√2 - 1)}
= (√3.√2 - 2√2 - √3 + 2)/{(√2)² - (1)²}
= (√6 - 2√2 - √3 + 2)/1
= √6 - 2√2 - √3 + 2
∴ x - 4 = √6 - 2√2 - √3 + 2 - 4
= √6 - 2√2 - √3 - 2
= -2√2 + √6 - √3 - 2
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