Question : A positive number, when decreased by 4, is equal to 21 times the reciprocal of this number. The number is:
Option 1: 3
Option 2: 7
Option 3: 5
Option 4: 9
Correct Answer: 7
Solution :
Let the positive numbers be $x$ and $\frac{1}{x}$.
According to the question,
$ x-4=\frac{21}{x}$
$x^{2}-4x-21 =0$
$x^{2}-7x+3x-21 =0$
$x(x-7)+3(x-7)=0$
$(x-7)(x+3) =0$
$x-7=0$ or $x+3=0$
$\therefore x=7$ or $x=-3$
$x$ cannot be –3, as it is a positive number.
Hence, the correct answer is 7.
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