Question

A positive number when decreased by 4 becomes 21 times its reciprocal. The number is 

(a) 8 

(b) 7 

(c) 6 

(d) 5

Answer 1

(b) 7

\(x\) - 4 = 21 x  \(\frac1x\)

⇒ x² - 4x = 21

⇒x² - 4x - 21 = 0 ⇒ (x - 7)(x + 3) = 0

⇒ x = 7, - 3  ⇒ x = 7.