If #x# and #y# are positive numbers, what is the minimum possible value of #(x+y)(1/x + 1/y)# ?
Original syntax:
If $x$ and $y$ are positive numbers, what is the minimum possible value of $(x+y)\left(\frac1x + \frac1y\right)?$
Original syntax:
If $x$ and $y$ are positive numbers, what is the minimum possible value of $(x+y)\left(\frac1x + \frac1y\right)?$
3 Answers
Four
Explanation:
Now, let's begin again. Suppose with some loss of generality that
What are the "extremee"?
Fortunately, all true paths lead to the same true consequence.
Explanation:
By symmetry
Now supposing
As we can observe the minimum value for
is
Explanation:
From the arithmetic mean-geometric mean inequality,
Thus,