Question

The roots of the equation $x+\frac{1}{x}=3\frac{1}{3},x\ne 0$, are

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

Answer 1

The correct option is B $3,\frac{1}{3}$

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

Multiply by $3x$ on both sides we get,

$3x^2+3=10x$

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

$3x^2-9x-x+3=0$

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

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

$\therefore x=\frac{1}{3}$ and $x=3$