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Question
Solve equation using factorisation method:
`x + 1/x = 2.5`
Solution
`x + 1/x = 2.5`
⇒ `(x^2 + 1)/x = 5/2`
⇒ 2x2 + 2 = 5x
⇒ 2x2 – 5x + 2 = 0
⇒ 2x(x – 2) – 1(x – 2) = 0
⇒ (x – 2)(2x – 1) = 0
Since x – 2 = 0 or 2x – 1 = 0
∴ x – 2 = 0
⇒ x = 2
∴ 2x – 1 = 0
⇒ 2x = 1
⇒ x = `1/2`
Then x = 2 or x = `1/2`
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