if X=1÷2-√3, then the value of x²-4x+1 is.
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Step-by-step explanation:
x² - 4x + 1 ⇒ (x - 2)² - 3
So, basically we have find the value of (x - 2)² - 3. Here,
x = 1/(2 - √3)
Rationalize the RHS:
⇒ x = (2 + √3)/(2 - √3)(2 + √3)
= (2 + √3)/(4 - 3) = 2 + √3
Hence,
⇒ (x - 2)² - 3
⇒ (2 + √3 - 2)² - 3 ⇒ (√3)² - 3
⇒ 3 - 3 ⇒ 0
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