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Question
Solve the following equation by factorization
`(2)/(x^2) - (5)/x + 2 = 0, x ≠ 0`
Solution
`(2)/(x^2) - (5)/x + 2 = 0, x ≠ 0`
⇒ 2 - 5x + 2x2 = 0
⇒ 2x2 - 5x + 2 = 0 ...`{(∵ 2 xx 2 = 4),(4 = -4 xx (-1)),(-5 = -4 - 1):}}`
⇒ 2x2 - 4x - x + 2 = 0
⇒ 2x(x - 2) - 1(x - 2) = 0
⇒ (x - 2) (2x - 1) = 0
Either x - 2 = 0,
then x = 2
or
2x = 1 = 0,
then 2x = 1
⇒ x = `(1)/(2)`
∴ x = 2, `(1)/(2)`.
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