If x+1x-34 - 2x+1x-32 – 8 = 0, then how many possible values can x have?
Explanation:
Let x+1x-32 = a
The given equation becomes: a2 – 2a – 8 = 0
⇒ (a - 4)(a + 2) = 0 ⇒ a = 4 or -2 (rejected since a has to be positive)
⇒ x+1x-32 = 4
Case 1: x+1x-3 = 2 ⇒ x + 1 = 2x – 6 ⇒ x = 7
Case 2: x+1x-3 = -2 ⇒ x + 1 = -2x + 6 ⇒ x = 5/3
∴ x can take 2 possible values i.e., 7 and 5/3.
Hence, 2.
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