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Question
Solve:
2x4 − 5x2 +3= 0, Take x2 = y
Sum
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Solution
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.
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