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Solving a Quadratic Equation by Completion of Squares Method

Solve: 2 x ...

Question

Solve: $2 x^{4} - 5 x^{2} + 3 = 0$

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Solution

Given: $2 x^{4} - 5 x^{2} + 3 = 0$

$⟹$ $2 x^{4} - 3 x^{2} - 2 x^{2} + 3 = 0$

$⟹$ $x^{2} (2 x^{2} - 3) - (2 x^{2} - 3) = 0$

$⟹ (x^{2} - 1) (2 x^{2} - 3) = 0$

$⟹ x^{2} = 1, \frac{3}{2}$

$⟹ x = \pm 1, \pm \sqrt{\frac{3}{2}}$

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