Thank you for registering.

One of our academic counsellors will contact you within 1 working day.

Please check your email for login details.
MY CART (5)

Use Coupon: CART20 and get 20% off on all online Study Material

ITEM
DETAILS
MRP
DISCOUNT
FINAL PRICE
Total Price: Rs.

There are no items in this cart.
Continue Shopping

If AM of two numbers be twice their GM then the numbers are in the ratio

If AM of two numbers be twice their GM then the numbers are in the ratio

Grade:12

2 Answers

SHAIK AASIF AHAMED
askIITians Faculty 74 Points
7 years ago

Hello student,
Please find the answer to your question below
Let the numbers be a,b
AM=(a+b)/2
GM= [sqrt{ab}]
Given AM=2GM
So (a+b)/2=2 [sqrt{ab}]
a+b-4 [sqrt{ab}] =0
Divide each term by b we get
(a/b)+1-4 [sqrt{a/b}] =0
([sqrt{a/b}] )2-4( [sqrt{a/b}] )+1=0
on solving quadratic equation we get
[sqrt{a/b}] =2 \pm[sqrt{3}]
So (a/b)=( [2\pmsqrt{3}] )2
(a/b)=7\pm[4sqrt{3}]
Khushi
14 Points
3 years ago

A.T.Q.

a + b / 2 = 2√ab

a + b = 4√ab

Squaring on both sides...

(a + b)² = 16ab ....(i)

a² + b² + 2ab = 16ab

a² + b² + 2ab - 16ab = 0

a² + b² - 14ab = 0

a² + b² - 2ab - 12ab = 0 

(a - b)² - 12ab = 0

(a - b)² = 12ab ....(ii)

Dividing (i) by (ii)

(a + b)² / (a - b)² = 16ab / 12ab

(a + b / a - b)² = 4/3

Square root on both sides...

a + b / a - b = 2 /√3

Using componento and dividendo ....

a + b + a - b / a + b - a + b = 2 + √3 / 2 - √3

2a / 2b = 2 + √3 / 2 - √3

a / b = 2 + √3 / 2 - √3

Hence proved.

Hope you can understand it.

Think You Can Provide A Better Answer ?

Provide a better Answer & Earn Cool Goodies See our forum point policy

ASK QUESTION

Get your questions answered by the expert for free