If A.M. and G.M. of two positive numbers...

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

Text Solution

Verified by Experts

The correct Answer is:

4, 16 OR 16, 4

Topper's Solved these Questions

SEQUENCE AND SERIES
KUMAR PRAKASHAN|Exercise Solutions of NCERT Exemplar Problems|13 Videos
SEQUENCE AND SERIES
KUMAR PRAKASHAN|Exercise Solutions of NCERT Exemplar Problems -Long Answer Type Question|4 Videos
SEQUENCE AND SERIES
KUMAR PRAKASHAN|Exercise Textbook based MCQs (Latest Exam MCQs)|3 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

The arithmetic and geometric mean of two positive numbers are 8 and 4 sqrt3 respectively. Find these numbers.

If A.M. and G.M. of roots of a quadratic equation are 8 and 5, respectively, then obtain the quadratic equation.

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)) .

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 )) .

The sum of the squares of two positive numbers is 233 and one number is 3 less than twice the other number. Find the numbers.

Statement 1 If a and b be two positive numbers, where agtb and 4xxGM=5xxHM for the numbers. Then, a=4b . Statement 2 (AM)(HM)=(GM)^(2) is true for positive numbers.

The G.M. of two positive numbers is 6. Their arithmetic mean A and harmonic mean H satisfy the equation 90A+5H=918 , then A may be equal to

Distance of two planets from the sun are 10^11 m and 10^(10) m respectively. Then find the ratio of time period of these two planets.

The sum of two numbers is 10 and their quotient is 2/3 . Find the numbers

During the propagation of one progressive harmonic wave having amplitude 10 m, displacements and particles at 2 m and 16 m at respectively 2s and 8 s are 5 m and 5 sqrt3 m respectively. Find angular frequency and wave vector for this wave.

KUMAR PRAKASHAN-SEQUENCE AND SERIES-Testbook Illustrations for Practice Work

If the sum of n terms of an A.P. is nP+1/2n(n-1)Q , where P and Q are...
Text Solution
|
The sum of n terms of two arithmetic progressions are in the ratio (3n...
Text Solution
|
The income of a person is Rs 3,00,000 in the first year and he receive...
Text Solution
|
Example 8 Insert 6 numbers between 3 and 24 such that the resulting se...
Text Solution
|
Find the 10^(th) and n^(th) terms of the G.P . 5, 25,125 ................
Text Solution
|
Which term of the G.P., 2,8,32, ... up to n terms is 131072 ?
Text Solution
|
In a GP the 3rd term is 24 and 6th term is 192. Find the 10th term.
Text Solution
|
Find the sum of first n terms and the sum of first 5 terms of the geom...
Text Solution
|
How many terms of the G.P.3,(3)/2,3/4 ..........are needed to give the...
Text Solution
|
The sum of first three terms of a G.P. is 13/12 and their product is –...
Text Solution
|
Find the sum of the sequence 7, 77, 777, 7777, ... to n terms.
Text Solution
|
A person has 2 parents, 4 grandparents, 8 great grandparents, and so o...
Text Solution
|
Insert three numbers between 1 and 256 so that the resulting sequence ...
Text Solution
|
If A.M. and G.M. of two positive numbers a and b are 10 and 8, respect...
Text Solution
|
Find the sum to n terms of the series : 5+11+19+29+41..........
Text Solution
|
Find the sum to n terms of the series whose n^("th") term is n (n+3).
Text Solution
|
If p^(th), q^(th), r^(th) and s^(th) terms of an A.P. are in G.P, the...
Text Solution
|
If a, b, c are in G.P. and a^(1/x) =b^(1/y)=c^(1/z) , prove that x, y...
Text Solution
|
If a, b, c, d and p are different real numbers such that (a^2 + b^2 + ...
Text Solution
|
If p,q,r are in G.P. and the equations, px^(2) + 2qx + r = 0 and dx^2+...
Text Solution
|