Math miscellaneousMedium
Question
Number of solutions of the equation ex(ex - 2) = 5|ex - 1| - 7 is -
Options
A.0
B.1
C.2
D.4
Solution
Put ex - 1 = t
⇒ (t + 1) (t - 1) = 5|t| - 7
⇒ t2 - 5|t| + 6 = 0
⇒ ex - 1 = ± 2; ex - 1 = ± 3
⇒ ex = 3; ex = 4 only ∴ 2 solutions.
⇒ (t + 1) (t - 1) = 5|t| - 7
⇒ t2 - 5|t| + 6 = 0
⇒ ex - 1 = ± 2; ex - 1 = ± 3
⇒ ex = 3; ex = 4 only ∴ 2 solutions.
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