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 po

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 po      Log On


   

Question 1207695: 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 MathLover1, greenestamps:
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

a+-+b+=+4+.......eq.1
a%5E2+-+b%5E2+=+8
%28a+-+b%29%28a%2Bb%29=+8....eq2, substitute a-b
4%28a%2Bb%29=+8
a%2Bb=+2........solve for b
b=2-a..........eq.2a

go to
a+-+b+=+4 .......eq.1, substitute b
a+-+%282-a%29+=+4+
a+-+2%2Ba+=+4+
2a=4%2B2
2a=6
a=3

go to
b=2-a..........eq.2a, substitute a
b=2-3
b=-1
solution: a=3, b=-1

(a) Find all possible values of ab
ab=3%28-1%29=-3

(b) Find all possible values of a%2Bb
a%2Bb=3%2B%28-1%29=2

(c) Find all possible values of a and b
a=3, b=-1


Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


a-b=4 [1]

a%5E2-b%5E2=8 [2]

Factor [2] and substitute [1]:

a%5E2-b%5E2=%28a%2Bb%29%28a-b%29=%28a%2Bb%29%284%29=8
a%2Bb=8%2F4=2 [3]

Add [1] and [3]:

2a=6
a=3 [4]

Substitute [4] in [3]:

3%2Bb=2
b=-1

Solution: a=3; b=-1

ANSWERS:
(a) ab = (3)(-1) = -3
(b) a+b = (3)+(-1) = 2
(c) a=3; b=-1