polynomials doubt-4

@Arnab: consider this: a=-1, b=1, c=-1, d=1

Infinite solutions!

unless something else is given!

Soluton is of form:

a = -d = m
b = -c = n (≥m)

m and n are are non-negative number! :D

a+b+c+d=0

what do u infer?

The best inference is at least one number has a different sign as the other numbers..

We can also infer..
The 4 nos can be separated into 2 groups such the 2 nos in a group has the same absolute value but different sign.. the grouping can be done in 3 ways i.e.
(a,b)(c,d) or (a,c)(b,d) or (a,d)(b,c)
.. so we will have to look for more hints..

Next is a²+b²=c²+d²

Thus, a has same absolute value as c or d!
so now there can be two types of groupings i.e. (a,c)(b,d) or (a,d)(b,c)

and the last set of clues finishes it! :D
a<b and c<d [1]

thus a must have a value less than b
a=m and b=n
m≤n
so -n≤-m
thus c=-n and d=-m

thus a=-d=m
and b=-c=n(≥m)

and as considered, m and n are + nos.

That is only one type of soln.. many more possible!

yo man! Thats the spirit Chinmaya! [1]

Cheers!!