Question

The sum of a number and its reciprocal is $\frac{17}{4}$. Then the number is $4$ or $\frac{1}{4}$.

• A. True
• B. False

Answer 1

The correct option is A True

$\Rightarrow$ Let the number be $x$, then it's reciprocal will be $\frac{1}{x}.$

According to the question,

$\Rightarrow$ $x+\frac{1}{x}=\frac{17}{4}$

$\Rightarrow$ $4x^2+4=17x$ [ Multiplying both sides by $4x$ ]

$\Rightarrow$ $4x^2-17x+4=0$

$\Rightarrow$ $4x^2-16x-x+4=0$

$\Rightarrow$ $4x(x-4)-1(x-4)=0$

$\Rightarrow$ $(x-4)(4x-1)=0$

$\Rightarrow$ $x-4=0$ or $4x-1=0$

$\therefore$ $x=4$ or $x=\frac{1}{4}$

$\therefore$ The required number is $4$ or $\frac{1}{4}$

Hence, the given statement is $True$.