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Kvant 2023
M2738
M2738
Part of
Kvant 2023
Problems
(1)
Roots of some cubics
Source: Kvant Magazine No. 3 2023 M2738
1/9/2024
The real numbers
a
1
,
a
2
,
a
3
a_1,a_2,a_3
a
1
,
a
2
,
a
3
and
b
b{}
b
are given. The equation
(
x
−
a
1
)
(
x
−
a
2
)
(
x
−
a
3
)
=
b
(x-a_1)(x-a_2)(x-a_3)=b
(
x
−
a
1
)
(
x
−
a
2
)
(
x
−
a
3
)
=
b
has three distinct real roots,
c
1
,
c
2
,
c
3
.
c_1,c_2,c_3.
c
1
,
c
2
,
c
3
.
Determine the roots of the equation
(
x
+
c
1
)
(
x
+
c
2
)
(
x
+
c
3
)
=
b
.
(x+c_1)(x+c_2)(x+c_3)=b.
(
x
+
c
1
)
(
x
+
c
2
)
(
x
+
c
3
)
=
b
.
Proposed by A. Antropov and K. Sukhov
algebra
roots