Difference between revisions of "1969 IMO Problems/Problem 2"
Durianaops (talk | contribs) m |
|||
Line 3: | Line 3: | ||
==Solution== | ==Solution== | ||
− | + | Because the period of <math>cos(x)</math> is <math>2\pi</math>, the period of <math>f(x)</math> is also <math>2\pi</math>. | |
+ | <cmath>f(x_1)=f(x_2)=f(x_1+x_2-x_1)</cmath> | ||
+ | We can get <math>x_2-x_1 = 2k\pi</math> for <math>k\in N^*</math>. Thus, <math>x_2-x_1=m\pi</math> for some integer <math>m.</math> | ||
==See Also== | ==See Also== | ||
{{IMO box|year=1969|num-b=1|num-a=3}} | {{IMO box|year=1969|num-b=1|num-a=3}} |
Revision as of 08:30, 12 March 2019
Problem
Let be real constants,
a real variable, and
Given that
prove that
for some integer
Solution
Because the period of is
, the period of
is also
.
We can get
for
. Thus,
for some integer
See Also
1969 IMO (Problems) • Resources | ||
Preceded by Problem 1 |
1 • 2 • 3 • 4 • 5 • 6 | Followed by Problem 3 |
All IMO Problems and Solutions |