Q. 615.0( 2 Votes )

If A and G be A.M. and G.M. respectively between two positive numbers, prove that the numbers are A ± .

Answer :

Let the two positive numbers be a and b.

Therefore, A = ⇒ a + b = 2A

and G = ⇒ ab = G2

The equation whose roots are a and b is

x2 – (a + b)x + ab = 0

⇒x2 – 2Ax + G2 = 0 …….(i)

or x =

      = A ±

      = A ±

The roots of (i) are a and b,

Hence, the two positive number are given by

A ±

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Interactive quiz on inequalities involving AM and GM45 mins
Check Your progress Part 2| Interactive Quiz: Sequence & Series47 mins
Sequence & Series (Lecture 1)56 mins
Sequence & Series (Lecture 5)42 mins
Sequence & Series (Lecture 7)37 mins
Check Your progress Part 3| Interactive Quiz: Sequence & Series46 mins
Sequence & Series (Lecture 8)35 mins
Sequence & Series (Lecture 6)42 mins
Use of sigma in finding sum42 mins
Trigonometric Series45 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
view all courses