0

Guest

Courses New

If a,b,c,d are in HP then ab+bc+cd =? a)3ad b)(a+b)(c+d) c)ac

If a,b,c,d are in HP then  ab+bc+cd =?
a)3ad   b)(a+b)(c+d)  c)ac  

Grade:11

1 Answers

Arun
25750 Points
6 years ago
Dear Shiv
 
 
a,b,c,d are in H.P
so (1/a),(1/b),(1/c),(1/d) are in A.P
d=(1/b)-(1/a)=(1/c)-(1/b)=(1/d)-(1/c)=x..........eq(1)
now (1/b)-(1/a)=(1/c)-(1/b)=(1/d)-(1/c)
=(a-b)/ab=(b-c)/bc=(c-d)/cd=(a-b+b-c+c-d)/(ab+bc+cd) by addendo
=(a-d)/(ab+bc+cd)
taking ad common
(1/b)-(1/a)=ad{(1/d)-(1/a)}/(ab+bc+cd)......... eq(2)
as we know
an=a1+(n-1)d
put n=4
a4=a1+(4-1)d
putting a4=1/d , a1=1/a , d=x
1/d=1/a+3x
put this in eq(2)
(1/b)-(1/a)=ad{(1/a)+3x-(1/a)}/(ab+bc+cd)
x=3adx/(ab+bc+cd)
ab+bc+cd=3ad
 
 
Regards
Arun(askIITians forum expert)

Think You Can Provide A Better Answer ?

Other Related Questions on Algebra

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