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Topic: Please help with equation!
Replies: 3   Last Post: Jul 10, 1996 10:29 AM

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Posts: 3
Registered: 12/12/04
Please help with equation!
Posted: Jul 8, 1996 11:54 PM
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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

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