Question

Find n if 2P(n, 2) + 50 = P(2n, 2)

Answer 1

Answer:

Hii!!

Step-by-step explanation:

2p(n,2)+50=p(2n,2)

2*n/n-2+50=2n/2n-2

2n(n-1)+50=2n(2n-1)

2 n square - 2 n + 50 = 4 n square - 2n

2n square - 50=0

2n square =50

N square =25

N=5

Hope it help you :-)

Answer 2

The value of n is 5.

Step-by-step explanation:

Consider the provided information.

According to permutation rule: $^nP_r=\frac{n!}{(n-r)!}$

Therefore the provided expression can be written as:

$2\times\frac{n!}{(n-2)!}+50=\frac{2n!}{(2n-2)!}$

Expand the term as shown:

$2\times\frac{1\times2\times3\times...(n-2)(n-1)n}{(n-2)!}+50=\frac{1\times2 \times....(2n-2)(2n-1)2n}{(2n-2)!}$

$2\times\frac{(n-2)! (n-1)n}{(n-2)!}+50=\frac{(2n-2)!(2n-1)2n}{(2n-2)!}$

$2n(n-1)+50=2n(2n-1)$

$2n^2 - 2n + 50 = 4n^2 - 2n,\\2n^2 = 50\\n^2 = 25\\n=5$

Hence, the value of n is 5.

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