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MAA AMC
AMC 12/AHSME
1980 AMC 12/AHSME
8
Number of Solutions
Number of Solutions
Source:
December 30, 2005
quadratics
algebra
quadratic formula
Problem Statement
How many pairs
(
a
,
b
)
(a,b)
(
a
,
b
)
of non-zero real numbers satisfy the equation
1
a
+
1
b
=
1
a
+
b
?
\frac{1}{a} + \frac{1}{b} = \frac{1}{a+b}?
a
1
+
b
1
=
a
+
b
1
?
(A) none
(B)
1
(C)
2
(D) one pair for each
b
≠
0
\text{(A)} \ \text{none} \qquad \text{(B)} \ 1 \qquad \text{(C)} \ 2 \qquad \text{(D)} \ \text{one pair for each} ~b \neq 0
(A)
none
(B)
1
(C)
2
(D)
one pair for each
b
=
0
(E) two pairs for each
b
≠
0
\text{(E)} \ \text{two pairs for each} ~b \neq 0
(E)
two pairs for each
b
=
0
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