Look. If the problem were so easy as to be solvable by mechanically pushing keys on a gadget, there would have no need for great_math to post it at all. If you had taken a look at the problems that great_math usually posts here, you should have realized that great_maths problems are usually more sophisticated than that.
If your mathematical ability is limited to pushing keys on your calculator, I suggest you take a good look around at what constitutes a good mathematical proof. You might learn something.
Perhaps you should re-read the first sentence of my reply to you.
Be careful not to confuse recognition of the usefulness of a calculator with reliance on a calculator.
]]>If your mathematical ability is limited to pushing keys on your calculator, I suggest you take a good look around at what constitutes a good mathematical proof. You might learn something.
]]>You are NOT supposed to use a calculator in this problem!!
Have you ever given any consideration to leaving your arrogance and anger at the login screen? The OP did not list any such restrictions on the problem. My method is perfectly legitimate. If you have a different way, fine. I have no doubt I could also find other ways to do it. However, I posted what, thus far, appears to be the easiest way to go about it.
]]>Here is my solution.
Note that the function
is strictly increasing for .Hence, for all
, .Now define
Then
.Since
for all , we have by above.Thus
is strictly decreasing for .In particular,
.But
.]]>From there, both expressions can be easily reduced to numerical values.
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