Question

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Answer 1

Answer:

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Step-by-step explanation:

n+r

P = (n+r)! / (n+r-2)!

2

= (n+r)! / (n+r-2)!

= (n+r)(n+r-1)(n+r-2)!

------------------------------

(n+r-2)!

= (n+r)(n+r-1)

=[(n+r)^2 - 1] .....(1)

Also,

n-r

P = (n-r)! / (n-r-2)!

2

= (n - r)! / (n - r-2)!

= (n-r)(n-r-1)(n - r-2)!/(n - r-2)!

= (n-r)(n-r-1)

= [(n-r)^2 -1] ....(2)

(1)-(2) :

4nr = 110 - 20 = 90

2nr = 45

From (1),

[(n+r)^2 - 1] = n^2 + r^2 + 45-1 = 110

Or, n^2 + r^2 = 110-44 = 66

So, (n+r)^2 = 66 + 45 = 111

From (1),

[(n-r)^2 - 1] = n^2 + r^2 - 45-1 = 20

(n-r)^2 = 66