NumericalModerate3 marks
Using properties of proportion, solve for x. Given that x is positive: (2x + √(4x² - 1)) / (2x - √(4x² - 1)) = 4
Topic: Shares, dividend and return
Previous-year question practice database
Answer
Exam answer
x =
Explanation
2x + √4x2 − 1 2x − √4x2 − 1 = 4 By using the property Componendo & Dividendo 2x + √4x2 − 1 + 2x − √4x2 − 1 2x + √4x2 − 1 − 2x − √4x2 − 1 = 4 + 1 4 − 1 ⇒ 4x 2√4x2 − 1 = ⇒ 2x √4x2 − 1 = Squaring both sides 4x2 4x2 − 1 = ⇒ 36x2 = 100x2 − 25 ⇒ 65x2 = 25 ⇒ x2 = ⇒ x = ± ∴ x =
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