Question

If a,b,c are three consecutive numbers, prove that (a-i)(a+1)(c-i)(c+i) = b^4 +1

Answer 1

let a be 1, b be 2 and c be 3 and I be 0

ATQ,

(a-i)(a+1)(c-i)(c+i)=b^4+1

=(1-0)(1+1)(3-0)(3+0)-1=2^4+1

=17=17

l.h.s =rhs

hence proved