0

Guest

Courses New

sum of squares of three distinct real numers which are in G.P id S^2. If their sum is alphaS, show that alpha^2 belongs to {1/3,1}u{1,3}.Please elaborate.

sum of squares of three distinct real numers which are in G.P id S^2. If their sum is alphaS, show that alpha^2 belongs to {1/3,1}u{1,3}.Please elaborate.

Grade:11

1 Answers

Vikas TU
14149 Points
7 years ago
sum of squares of three distinct real numers which are in G.P is:
S^2 = a^2 + (ar)^2 + (ar^2)^2
        = a^2(1 + r^2 + r^4) 
        =a^2(1.(r^2)^3 – 1)/(r^2 – 1)..................(1)
 
Sum is alpha,
a(1 + r + r^2) = alphaS ................(2)
substituting the eqn. (2) in (1) with value of a and solvng for r that is common ration whic wwould always lie between -1 to 1.
The interval for alpha^2 which would always be postive lies in
{1/3, 1) U {1,3).
 

Think You Can Provide A Better Answer ?

Other Related Questions on Algebra

View all Questions »

ASK QUESTION

Get your questions answered by the expert for free

Answer and earn gift vouchers

Win Gift vouchers upto Rs 500/-

View courses by askIITians

Design classes One-on-One in your own way with Top IITians/Medical Professionals

Click Here Know More

Complete Self Study Package designed by Industry Leading Experts

Click Here Know More

Live 1-1 coding classes to unleash the Creator in your Child

Click Here Know More

a Complete All-in-One Study package Fully Loaded inside a Tablet!

Click Here Know More