Question

Solve:

2x⁴ − 5x² +3= 0, Take x² = y

Answer 1

Let x² = y,

⇒ 2x⁴ − 5x² + 3 = 0

⇒ 2y² − 5y + 3 = 0

⇒ 2y² − 2y − 3y + 3 = 0

⇒ 2y(y − 1) − 3(y − 1) = 0

⇒ (2y − 3)(y − 1) = 0

⇒ 2y − 3 = 0 or y − 1 = 0 [Zero product rule]

⇒ 2y = 3 or y = 1

⇒ y = `3/2`​ or y = 1.

∴ x² = `3/2`​ or x² = 1

⇒ x = `+- sqrt(3/2) = +- 1.22 or sqrt 1 = +- 1`

Hence, x = +1.22, −1.22, +1, −1.