Question

If
\[\huge {1\over z} = {1 \over x } + {1 \over y}\]
and x>y>0
prove that z 12 years ago

Answer 1

if
\[\huge {1\over z }= {1 \over x} + {1 \over y} \]
and x>y>0
prove that z<y

Answer 2

Since \(x,y>0\), we know that \(1/x+1/y>1/y\). So \(1/z>1/y\), so \(z>y\).

Answer 3

another way to prove this is
1/z = 1/x + 1/y = (x+y)/(xy)
then z = (xy)/(x+y)

since x,y > 0, (xy)/(x+y) < (xy)/x = y
so z < y

Answer 4

thank you guys :)