Question 1207740
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Let a and b be real numbers. For this problem, assume that a - b = 4 and a^2 - b^2 = 8.
(a) Find all possible values of ab
(b) Find all possible values of a+b
(c) Find all possible values of a and b
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Factor a^2- b^2 = 8 into

    (a-b)*(a+b) = 8.


Replace here a-b by 4, since it is given.  You will get

    4*(a+b) = 8.


It implies 

    a + b = 8/4 = 2.


Now you have two linear equations for "a" and "b"

    a + b = 2,

    a - b = 4.


Add them and get  2a = 6;  hence  a = 6/2 = 3.

Subtract them and get  2b = 2 - 4 = -2;  hence  b = -2/2 = -1.


Now  ab = 3*(-1) = -3;        <---- answer to (a)

     a + b = 3 + (-1) = 2;    <---- answer to (b)

     a = 3;  b = -1.          <---- answer to (c).
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Solved.