if a,b,c are distinct positive real in H.P then the value of the expression b+a/b-a + b+c/b-c is Share with your friends Share 8 Vijay Kumar Gupta answered this Note that a harmonic progression is a progression in which the reciprocal of the terms are in arithmetic progression.For example, the following series is in harmonic progression. 12, 14, 16,18,...Note that the reciprocal of the terms are 2, 4, 6, 8,... which is in arithmetic progression.Now it is given that a, b, c are in harmonic progression.This implies that 1a, 1b, 1c are in arithmetic progression.So twice the middle term equals the sum of extreme terms. 21b=1a+1c 2b=a+cac b2=aca+c b=2aca+c .....(1)It is required to find the value of the expression. b+ab-a+b+cb-c Apply componendo and dividendo = b+a+b-ab+a-b-a+b+c+b-cb+c-b-c = b+a+b-ab+a-b+a+b+c+b-cb+c-b+c = 2b2a+2b2c = b1a+1c = ba+cacPut the value from (1) to get, b+ab-a+b+cb-c= 2aca+ca+cac = 2Thus the required value is 2 24 View Full Answer Parth Tiwari answered this . b+a/b-a + b+c/b-c Applying componendo and dividendo b+a+b-a/b+a-b+a + b+c+b-c/b+c-b+c 2b/2a + 2b/2c = bc + ba/ac = b (a+c)/ac 1
