SOLUTION: 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 pos

Algebra ->  Systems-of-equations -> SOLUTION: 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 pos      Log On


   

Question 1207740: 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
Found 2 solutions by mccravyedwin, ikleyn:
Answer by mccravyedwin(407) About Me  (Show Source):
You can put this solution on YOUR website!
system%28a+-+b+=+4%2Ca%5E2+-+b%5E2+=+8%29

a=b%2B4

%28b%2B4%29%5E2-b%5E2=8

b%5E2%2B8b%2B16-b%5E2=8
8b%2B16=8
b%2B2=1
b=-1
a=b%2B4
a=-1%2B4
a=3

Since 
(c) the only possible values of a and b are 3 and -1, respectively, then
(a) the only possible value for ab is (3)(-1) = -3, and
(b) the only possible value for a+b is (3)+(-1) = 2.

Edwin

Answer by ikleyn(52780) About Me  (Show Source):
You can put this solution on YOUR website!
.
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
~~~~~~~~~~~~~~~~~~~ 

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).

Solved.