Question
A number is 2/5 more than 33 times its reciprocal. What is
the number?Solution
ATQ,
Let the number be x.
x – 33/x = 2/5
⇒ (x² – 33)/x = 2/5
Cross-multiplying:
5x² – 165 = 2x
⇒ 5x² – 2x – 165 = 0
Factorizing:
5x² – 25x + 23x – 165 = 0
5x(x – 5) + 33(x – 5) = 0
(5x + 33)(x – 5) = 0
So, x = –33/5 or x = 5
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