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Contests
National and Regional Contests
USA Contests
MAA AMC
AMC 12/AHSME
1966 AMC 12/AHSME
3
AM-GM
AM-GM
Source:
March 9, 2006
Problem Statement
If the arithmetic mean of two numbers is
6
6
6
and thier geometric mean is
10
10
10
, then an equation with the given two numbers as roots is:
(A)
x
2
+
12
x
+
100
=
0
(B)
x
2
+
6
x
+
100
=
0
(C)
x
2
−
12
x
−
10
=
0
\text{(A)} \ x^2+12x+100=0 ~~ \text{(B)} \ x^2+6x+100=0 ~~ \text{(C)} \ x^2-12x-10=0
(A)
x
2
+
12
x
+
100
=
0
(B)
x
2
+
6
x
+
100
=
0
(C)
x
2
−
12
x
−
10
=
0
(D)
x
2
−
12
x
+
100
=
0
(E)
x
2
−
6
x
+
100
=
0
\text{(D)} \ x^2-12x+100=0 \qquad \text{(E)} \ x^2-6x+100=0
(D)
x
2
−
12
x
+
100
=
0
(E)
x
2
−
6
x
+
100
=
0
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