if a^ (n)-b^(n)=d^(2)-c^(2)
where a,b,n are given which are natural numbers
what is the relation between a,b,c & d
c and d can be rational numbers also.
2006-07-13 20:46:21 · 6 answers · asked by rajesh bhowmick 2 in Science & Mathematics ➔ Mathematics
7 ^ (3) - 4 ^ (3) = 48 ^ (2) - 45 ^ (2)
2006-07-14 00:09:29 · update #1
d^2-c^2=(d-c)(d+C)
a^n-b^n is divisible by (a-b)
a-b is a natural number.
2006-07-13 21:18:19 · answer #1 · answered by Ash 2 · 0⤊ 0⤋
One easy solution:
Factorize,
a^n-b^n = (a-b)*(a^(n-1)+a^(n-2)*b+a^(n-...
Therefore (since c and d are allowed to be rational),
d-c = a-b
d+c = a^(n-1)+a^(n-2)*b+a^(n-3)*b^2+...
Or you can have
d+c = a-b
d-c = a^(n-1)+a^(n-2)*b+a^(n-3)*b^2+...
So, d = sum/2; c = difference/2.
You seem to be asking the same ques several times!!!
2006-07-14 12:28:57 · answer #2 · answered by robo 1 · 0⤊ 0⤋
a-b = d-c
(a-b) / (d-c) = 1
2006-07-14 12:40:45 · answer #3 · answered by Brenmore 5 · 0⤊ 0⤋
a & b are directely proporsanal to d & c
because a & b , n are natural number and it is divide by d & c
2006-07-14 05:03:33 · answer #4 · answered by thakur4u5 2 · 0⤊ 0⤋
Since a^ (n)-b^(n) is divisible by (a-b)
an d^(2)-c^(2) = (d+c)(d-c)
we can infer that (a-b) is directly propotional to (b-c)
:)
2006-07-14 05:31:07 · answer #5 · answered by Maninder 2 · 0⤊ 0⤋
im not even gonna think of it, its a wild goose chase, a and b are not given and there is no way to figure out what they are
2006-07-14 03:51:24 · answer #6 · answered by Dorkchop 2 · 0⤊ 0⤋