If p2-4 p-5-2-2 p-3-p-2- then the number of values of p isA- 0B- 2C- 1D- 3

The correct option is C 1Here, p^2 4p+5=2p 3 ⇒ p^2 6p+8=0 ⇒ p^2 4p 2p+8=0 ⇒ (p 4)(p 2)=0 ⇒ p=2,4 ...(1) Also, 2=|p 2| ⇒ p=0,4 ...(2) Value of p common fro ...

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Standard XII

Mathematics

Ordered Pair

If p2-4 p+5,2...

Question

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

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Solution

The correct option is B $1$
Here, $p^{2} - 4 p + 5 = 2 p - 3$
$\Rightarrow p^{2} - 6 p + 8 = 0$
$\Rightarrow p^{2} - 4 p - 2 p + 8 = 0$
$\Rightarrow (p - 4) (p - 2) = 0$
$\Rightarrow p = 2, 4 . . . (1)$
Also,
$2 = | p - 2 |$
$\Rightarrow p = 0, 4 . . . (2)$

Value of $p$ common from $(1)$ and $(2)$ is $p = 4$
$∴$ There is only one value of $p$

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If (p2−4p+5,2)=(2p−3,|p−2|), then the number of values of p is

The correct option is B 1Here, p2−4p+5=2p−3 ⇒p2−6p+8=0 ⇒p2−4p−2p+8=0 ⇒(p−4)(p−2)=0 ⇒p=2,4 ...(1) Also, 2=|p−2| ⇒p=0,4 ...(2) Value of p common from (1) and (2) is p=4 ∴There is only one value of p

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