Home
Class 11
MATHS
If A and G be A.M. and G.M., respectivel...

If A and G be A.M. and G.M., respectively between two positive numbers, prove that the numbers are `A pm sqrt((A+G )(A−G ))` .

Promotional Banner

Topper's Solved these Questions

  • SEQUENCE AND SERIES

    KUMAR PRAKASHAN|Exercise Solutions of NCERT Exemplar Problems -Matching The Columns|2 Videos
  • RELATIONS AND FUNCTIONS

    KUMAR PRAKASHAN|Exercise Solutions of NCERT Exemplar Problems (Question of Module)|16 Videos
  • SETS

    KUMAR PRAKASHAN|Exercise QUESTION OF MODULE|28 Videos

Similar Questions

Explore conceptually related problems

If A.M. and G.M. of two positive numbers a and b are 10 and 8, respectively, find the numbers.

If A be one A.M and p, q be two G.M.'s between two numbers then 2A is equal to…..

The ratio of the A.M. and G.M. of two positive numbers a and b, is m : n. Show that a:b =(m+sqrt(m^2-n^2)):(m-sqrt(m^(2)-n^2)) .

Find two positive numbers whose difference is 12 and whose A.M. exceeds the G.M. by 2.

If A is the arithmetic mean and G_(1), G_(2) be two geometric mean between any two numbers, then prove that 2A = (G_(1)^(2))/(G_(2)) + (G_(2)^(2))/(G_(1))

The (m+n)^(th) and (m-n)^(th) terms of a G.P. are p and q respectively. Show that the m^(th) and n^(th) terms are sqrtpq and p((q)/(p))^((m)/(2n)) respectively.

The A.M of two positive number is x and two G.M.'s between them are y and z. Then (y^(3) + z^(3))/(xyz) = …….

If A is the arithmatic mean and G_(1) and G_(2) be two geometric means between any two numbers then prove that, (G_(1)^(2))/(G_(2)) + (G_(2)^(2))/(G_(1))=2A

If E , M , J , and G , respectively , denote energy , mass , angular momentum , and gravitational constant , then EJ^(2) //M^(5) G^(2) has the dimensions of