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Algebra - 2

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by Aman verma » Wed Jun 02, 2010 9:34 am
Q: The value of 1/(1 + p + q^-1) + 1/(1 + q + r^-1) + 1/(1 + r + p^-1), given that pqr = 1, is :

a)1

b)0

c)pqr

d)p+q+r

e)-1
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by akdayal » Wed Jun 02, 2010 12:04 pm
Ans is (a) 1.
similar to https://www.beatthegmat.com/algebra-1-t58826.html
do the same steps.
brings any two denominator into one denominator by taking common and using the condition.
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by Aman verma » Thu Jun 03, 2010 8:05 am
OAA.Thanks AKDAYAL but can you elaborate. I tried to solve it that way ,but unable to reach the answer. I must have screwed up somewhere.
Last edited by Aman verma on Fri Jun 04, 2010 1:09 am, edited 1 time in total.
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by akdayal » Thu Jun 03, 2010 9:04 am
OAA.Thanks AKDAYAL but can you elaborte. I tried to solve it that way ,but unable to reach the answer. I must have screwed up somewhere.
Here is explanation:
1st term: 1/(1 + p + 1/q) = q/(q + pq + 1) = q/(q + 1/r + 1) [ given pqr = 1]
2nd term 1/(1 + q + 1/r)
3rd term 1/(1 + r + 1/p) = p/(p + pr + 1) = p/(p + 1/q + 1) [pr = 1/q]
Now p/(p + 1/q + 1) = pq/(pq + 1 + q) = (1/r)/(1/r + 1 + q)
Now add these three terms :
q/(q + 1/r + 1) + 1/(1 + q + 1/r) + (1/r)/(1/r + 1 + q) = (q + 1 + 1/r)/(q + 1 + 1/r) = 1
Hope this will help.
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