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National and Regional Contests
Russia Contests
All-Russian Olympiad Regional Round
2010 All-Russian Olympiad Regional Round
10.5
10.5
Part of
2010 All-Russian Olympiad Regional Round
Problems
(1)
cx^2-bx + a > cx-b if ax^2+bx+c > cx
Source: Russian Regional Olympiad 2010 10.5
8/24/2024
Non-zero numbers
a
,
b
,
c
a, b, c
a
,
b
,
c
are such that
a
x
2
+
b
x
+
c
>
c
x
ax^2+bx+c > cx
a
x
2
+
b
x
+
c
>
c
x
for any
x
x
x
. Prove that
c
x
2
−
b
x
+
a
>
c
x
−
b
cx^2-bx + a > cx-b
c
x
2
−
b
x
+
a
>
c
x
−
b
for any
x
x
x
.
algebra
inequalities