Question

If $x$ and $y$ are the two values of $t$ that satisfy the equation $t^2-6t+8=0$, with $y<x$, find the value of $x-y$

• A. $2$
• B. $4$
• C. $6$
• D. $8$
• E. $10$

Answer 1

The correct option is A $2$

$t^2-6t+8=0$

$\Rightarrow t^2-4t-2t+8=0$
$\Rightarrow t(t-4)-2(t-4)=0$

$\Rightarrow (t-4)(t-2)=0$

$\Rightarrow t-4=0$ or $t-2=0$

$\Rightarrow t=4,2$

According to the question $y<x$, so

$x=4,y=2$

$\therefore x-y=4-2=2$