QQuestion
Solve: (2x + 1) + \frac{3}{(2x + 1)} = 4, (x ≠ −1/2)
✓Answer
Let 2x + 1 = a
a + \frac{3}{a} = 4
⇒ a² + 3 = 4a
⇒ a² – 4a + 3 = 0
⇒ a² – (3 + 1)a + 3 = 0
⇒ a² – 3a – a + 3 = 0
⇒ (a – 1)(a – 3) = 0
So, a = 1 or a = 3
For a = 1: 2x + 1 = 1 ⇒ x = 0
For a = 3: 2x + 1 = 3 ⇒ x = 1
∴ x = 0 or x = 1
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