Question

If the sum of a number and its reciprocal is $\frac{10}{3}$, then the numbers are

• A. $4,\frac{1}{4}$
• B. $3,\frac{1}{3}$
• C. $-4,-\frac{1}{4}$
• D. $-3,-\frac{1}{3}$

Answer 1

Answer: (B)

$3,\frac{1}{3}$

Let the number be $x$

then $x+\frac{1}{x}=\frac{10}{3}$

$\Rightarrow x^2+1=\frac{10}{3}x$

$\Rightarrow 3x^2+3=10x$

$\Rightarrow 3x^2-10x+3=0$

$\Rightarrow 3x^2(x-3)-1(x-3)=0$

$\Rightarrow (x-3)$ $(3x-1)=0$

$\Rightarrow x=3,\frac{1}{3}$

The number is $3$ or $\frac{1}{3}$