Question

Solve the following equation by reducing it to quadratic equation:
`sqrt(3x^2 - 2) + 1 = 2x`.

Answer 1

`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].