Question

$Ifx-\frac{1}{x}=\frac{15}{4},\text{then}x+\frac{1}{x}$=

• A. 4
• B. $\frac{17}{4}$
• C. $\frac{13}{4}$
• D. $\frac{1}{4}$

Answer 1

Answer: (B)

$x-\frac{1}{x}=\frac{15}{4}{(x+\frac{1}{x})}^2={(x-\frac{1}{x})}^2+4={\left(\frac{15}{4}\right)}^2+4=\frac{225}{16}+4=\frac{225+64}{16}=\frac{289}{16}={\left(\frac{17}{4}\right)}^2\therefore x+\frac{1}{x}=\frac{17}{4}$