Math, asked by junnu123, 1 year ago

If a,b,c,d are four consecutive integers, prove that √abcd+1 is a rational number.

Answers

Answered by rational
1
Let the four consecutive integers a,b,c,d be n,~n+1,~n+2,~n+3 and consider 
n(n+1)(n+2)(n+3)+1

As 1+2~=~0+3n(n+1)(n+2)(n+3)+1 = \underbrace{n(n+3)}\underbrace{(n+1)(n+2)}+1~=~(n^2+3n)(n^2+3n+2)+1

Letting n^2+3n=k :
k(k+2)+1~=~k^2+2k+1~=~(k+1)^2

The squareroot of which is an integer.
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