0

ADNAN MUHAMMED

Grade 12,

Courses New

If a,b,c are in ap show that 1/√b+√c,1/√c+√a,1/√a+√b.

If a,b,c are in ap show that 1/√b+√c,1/√c+√a,1/√a+√b.

Grade:10

1 Answers

Arun
25750 Points
6 years ago
Dear Student
 
∵ a, b, c ... in AP. 

∴ 2b = a + c .......... (1) 

∴ To Prove : 1/(√b + √c), 1/(√c + √a), 1/(√a + √b) ... in AP 

⇒ To Prove : [ 1/(√c+√a) ] - [ 1/(√b+√c) ] = [ 1/(√a+√b) ] - [ 1/(√c+√a) ] 

⇒ To Prove : [ (√b-√a) / (√b+√c) ] = [ (√c-√b) / (√a+√b) ] 

⇒ To Prove : (√b-√a)·(√b+√a) = (√c-√b)·(√c+√b) 

⇒ To Prove : b - a = c - b 

⇒ To Prove : 2b = a + c, which is True ... from (1) 

Hence, the result.
 
Regards
Arun(askIITians forum expert)

Think You Can Provide A Better Answer ?

Other Related Questions on Magical Mathematics[Interesting Approach]

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