Question

If $a$ and $B$ are the roots of the equation $x^2-5x+6=0$, find the value of $m$ if $\frac{a}{B}+\frac{B}{a}$ is $\frac{13}{m}$.

Answer 1

Given equation is

$x^2-5x+6=0$
$(x-3)(x-2)=0$

$\therefore x=2,3$
Then, $a=2,B=3$

$\therefore \frac{a}{B}+\frac{B}{a}=\frac{2}{3}+\frac{3}{2}=\frac{13}{m}$

$=\frac{4+9}{6}$

$=\frac{13}{6}$

$\therefore m=6$