• Engineering and Architecture
  • Management and Business Administration
  • Medicine and Allied Sciences
  • Law
  • Animation and Design
  • Media, Mass Communication and Journalism
  • Finance & Accounts
  • Computer Application and IT
  • Pharmacy
  • Hospitality and Tourism
  • Competition
  • School
  • Study Abroad
  • Arts, Commerce & Sciences
  • Learn
  • Online Courses and Certifications
  1. Home
  3. Study Material
  4. Relation between A.M., G.M. and H.M. - Practice Questions & MCQ

Relation between A.M., G.M. and H.M. - Practice Questions & MCQ

Updated on Sep 18, 2023 18:34 AM

Quick Facts

  • 3 Questions around this concept.

Concepts Covered - 1

Properties of A.M. and G.M.

Properties of A.M. and  G.M

A and G are arithmetic and geometric mean of ‘a’ and ‘b’, two real, positive and distinct number. Then,

  • a and b are the roots of the equation x2-2Ax+G2=0.

  • a and b are given by A \pm \sqrt{(A+G)(A-G)}.

Proof:

\begin{array}{l}{A=\frac{a+b}{2} \Rightarrow 2 A=a+b} \\ {G=\sqrt{a b} \Rightarrow G^{2}=a b}\end{array}

a and b are the roots of the equation, then

\begin{array}{l}{x^{2}-2(\text { sum of roots) } x+\text { products of roots }=0} \\ {\Rightarrow x^{2}-(a+b)+a b=0} \\ {\Rightarrow x^{2}-2 A x+G^{2}=0}\end{array}

Roots of the equation are 

\begin{array}{l}{x=\frac{2 A \pm \sqrt{(-2 A)^{2}-4 \cdot 1 \cdot G^{2}}}{2}} \\ {{x}=A \pm \sqrt{(A+G)(A-G)}}\end{array}

Study it with Videos

Properties of A.M. and G.M.

Study other Related Concepts

Relation between A.M., G.M. and H.M. Current Topic

Sequence And Series
Arithmetic Progression
Sum of n Terms of an AP
Arithmetic Mean in AP
Geometric Progression
Geometric Mean In GP
Sum To n Terms Of a GP
Harmonic Progression
Harmonic Mean in HP
Relation between A.M., G.M. and H.M.

"Stay in the loop. Receive exam news, study resources, and expert advice!"

Books

Reference Books

Properties of A.M. and G.M.

Mathematics for Joint Entrance Examination JEE (Advanced) : Algebra

Page No. : 5.12

Line : 55

Clear your Basics with NCERT

Get Answer to all your questions

Download Careers360 App
All this at the convenience of your phone

  • Regular Exam Updates

  • Best College Recommendations

  • College & Rank predictors

  • Detailed Books and Sample Papers

  • Question and Answers

Scan and download the app

OR

Explore Top Colleges Accepting Applications
Back to top