Question

Find a positive number which exceeds sixty-five times its reciprocal by $64$

• A. $65$
• B. $75$
• C. $1$
• D. $-1$

Answer 1

Answer: (A), (D)

The correct options are
A $65$
D $-1$

$\Rightarrow$ Let the number be $x$

$\Rightarrow$ Sixty-five times of its reciprocal $=\frac{65}{x}$

According to the given condition,

$\Rightarrow$ $x-\frac{65}{x}=64$

$\Rightarrow$ $x^2-65=64x$

$\Rightarrow$ $x^2-64x-65=0$

$\Rightarrow$ $x^2-65x+x-65=0$

$\Rightarrow$ $x(x-65)+1(x-65)=0$

$\Rightarrow$ $(x-65)(x+1)=0$

$\Rightarrow$ $x-65=0$ and $x+1=0$

$\therefore$ $x=65$ and $x=-1$