Question

If $(p^2-4p+5,2)=(2p-3,|p-2|)$, then the number of values of $p$ is

• A. $0$
• B. $1$
• C. $2$
• D. $3$

Answer 1

The correct option is B $1$

Here, $p^2-4p+5=2p-3$
$\Rightarrow p^2-6p+8=0$
$\Rightarrow p^2-4p-2p+8=0$
$\Rightarrow (p-4)(p-2)=0$
$\Rightarrow p=2,4...\left(1\right)$
Also,
$2=|p-2|$
$\Rightarrow p=0,4...\left(2\right)$

Value of $p$ common from $\left(1\right)$ and $\left(2\right)$ is $p=4$
$\therefore$There is only one value of $p$