If x = √((2+√3)/(2-√3)) , then determine the value of x² + x - 9?
2025
If x = √((2+√3)/(2-√3)) , then determine the value of x² + x - 9?
- A.
3√3
- B.
5√3
- C.
7√3
- D.
9√3
Attempted by 11 students.
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Correct answer: B
Rationalizing gives (2 + sqrt3)/(2 - sqrt3) = 7 + 4sqrt3 = (2 + sqrt3)^2. Thus x = 2 + sqrt3, and x^2 + x - 9 = 5sqrt3.