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Please help with equation!
Posted:
Jul 8, 1996 11:54 PM


I ran across the following problem in a book and would like to solve it except I'm not sure what it's asking for:
Let a_1, a_2,...,a_n and b_1, b_2,..., b_n be given sets of real numbers. Determine necessary and sufficient conditions on a_i and b_i such that there are real constants A and B with the property that
(a_1*x + b_1)^2 + (a_2*x + b_2)^2 + ... + (a_n*x + b_n)^2 = (A*x + B)^2
for all values of x.
My question is, what does it mean to determine necessary and sufficient conditions for something? I would appreciate any hints on solving this and/or solutions you may have.
Billy Hung



