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Question
Solve the following equation by reducing it to quadratic equation:
`sqrt(3x^2 - 2) + 1 = 2x`.
Solution
`sqrt(3x^2 - 2) + 1 = 2x`
⇒ `sqrt(3x^2 - 2)`
= 2x - 1
On squaring both sides, we get
3x2 - 2 = 4x2 + 1 - 4x
⇒ -x2 + 4x - 3 = 0
⇒ x2 - 4x + 3 = 0
⇒ x2 - 3x - x + 3 = 0
⇒ x(x - 3) -1(x - 3) = 0
⇒ (x - 3) (x - 1) = 0
⇒ x = 3 or x = 1
Hence, the solutions are [3, 1].
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