Question
A number exceeds 40 times its reciprocal by 7/8. Determine
the number.Solution
ATQ,
Let the number be x.
x – 40/x = 7/8
⇒ (x² – 40)/x = 7/8
Cross-multiplying:
8x² – 320 = 7x
⇒ 8x² – 7x – 320 = 0
Factorizing:
8x² – 40x + 33x – 320 = 0
8x(x – 5) + 64(x – 5) = 0
(8x + 64)(x – 5) = 0
So, x = –8 or x = 5
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