Question
A number exceeds 45 times its reciprocal by 5/6. Find the number.
Solution
ATQ,
Let the number be x.
x – 45/x = 5/6
⇒ (x² – 45)/x = 5/6
Cross-multiplying:
6x² – 270 = 5x
⇒ 6x² – 5x – 270 = 0
Factorizing:
6x² – 30x + 25x – 270 = 0
6x(x – 5) + 27(x – 5) = 0
(6x + 27)(x – 10) = 0
So, x = –9/2 or x = 10
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