Question

B /
1.5) Solve any one sub question
n²–4 n²+4.
1) If n is even number and also n>2 then ( n,? =4 *+4) forms a Pythagorean
triplet. Prove it taking suitable value for n, form one triplet
ornare common tangents to two circles of unequal radii​

Answer 1

Answer:

Given n! /[2(n -2)!] : n!/[4!(n -4)!] = 2:1

=> [n! / 2! (n -2)!].[4! (n -4)! /n!] = 2/1

=> 4.3.2!.(n -4)! /[2!.(n -2).(n -3).(n -4)!] = 2/1

=> 4.3 /[(n -2)(n -3)] = 2/1

=> (n -2)(n -3) = 6

=> n² -5 n = 0 => n (n -5) = 0

=> n = 0 or n = 5

But, for n = 0, (n -2)! and (n -4)! are not meaningful, therefore, n = 5.