SOLUTION: Solve the equation {{{(matrix(2,1,n,2))}}}{{{""-""}}}{{{(matrix(2,1,n,1))}}}{{{""=""}}}{{{20}}} where n is a natural number

Algebra ->  Permutations -> SOLUTION: Solve the equation {{{(matrix(2,1,n,2))}}}{{{""-""}}}{{{(matrix(2,1,n,1))}}}{{{""=""}}}{{{20}}} where n is a natural number       Log On


   

Question 945597: Solve the equation %28matrix%282%2C1%2Cn%2C2%29%29%22%22-%22%22%28matrix%282%2C1%2Cn%2C1%29%29%22%22=%22%2220
where n is a natural number

Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
%28matrix%282%2C1%2Cn%2C2%29%29%22%22-%22%22%28matrix%282%2C1%2Cn%2C1%29%29%22%22=%22%2220

n%21%2F%282%21%2A%28n-2%29%21%29%22%22-%22%22n%21%2F%281%21%2A%28n-1%29%21%29%22%22=%22%2220

Replace n! by n*(n-1)*(n-2)! in the first fraction and by n*(n-1)! in the second 

%28n%2A%28n-1%29%2A%28n-2%29%21%29%2F%282%2A%28n-2%29%21%29%22%22-%22%22%28n%2A%28n-1%29%21%29%2F%281%28n-1%29%21%29%22%22=%22%2220

%28n%2A%28n-1%29%2Across%28%28n-2%29%21%29%29%2F%282%2Across%28%28n-2%29%21%29%29%22%22-%22%22%28n%2Across%28%28n-1%29%21%29%29%2F%281cross%28%28n-1%29%21%29%29%22%22=%22%2220

%28n%2A%28n-1%29%29%2F2%22%22-%22%22n%2F1%22%22=%22%2220

Multiply through by 2 to clear of fractions:

n%2A%28n-1%29-2n%22%22=%22%2240

n%5E2-n-2n%22%22=%22%2240

n%5E2-3n%22%22=%22%2240

n%5E2-3n-40%22%22=%22%22%220%22

%28n-8%29%28n%2B5%29%22%22=%22%22%220%22

n-8 = 0;  n+5 = 0
  n = 8     n = -5

Ignore negative answer.

Answer:  n = 8

Edwin