The three numbers ,

MATHEMATICS · Subjective · CBSE · Mathematics · Arithmetic Progressions · Arithmetic Progressions

Problem

The three numbers

x

,

y

, and

z

satisfy

x>y>z>0

. Show that if

\frac{1}{x}

,

\frac{1}{y}

, and

\frac{1}{z}

are consecutive terms of an arithmetic sequence, then

x-z

,

y

, and

x-y+z

can be the side lengths of a right-angled triangle.

Related theory

Browse the problem library