Question
If $x, y, z$ are in A.P., $a x, b y, c z$ in G.P. and $a, b, c$ in H.P. prove that $\frac{x}{z}+\frac{z}{x}=\frac{a}{c}+\frac{c}{a}$.
Step 1
P., we can write $2y = x + z$ ...(equation 1) Show more…
Show all steps
Your feedback will help us improve your experience
Sandip Ranjan and 94 other Calculus 2 / BC educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
If $a^{x}=b^{y}=c^{z}$ and $a, b, c$ be in G.P. then prove that $x, y, z$ are in H.P.
If $a^{\frac{1}{x}}=b^{\frac{1}{y}}=c^{\frac{1}{z}}$ and $a, b, c$ be in G.P. then prove that $x, y, z$ are in A.P.
Given $a^{x}=b^{y}=c^{z}=d^{u}$ and $a, b, c, d$ are in G.P., show that $x, y, z, u$ are in H.P.
Transcript
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD