If a, b, c are in HP, then what is 1 b-a + 1 b-c equal to? 1. 2 b 2. 1 a + 1 c 3. 1 2 ( 1 a + 1 b + 1 c ) Select the correct answer using the code given below:

Step-by-step solution

a, b, c are in H.P. 2 b = 1 a + 1 c aligned & b= 2 a c a+c & b-a= 2 a c a+c -a= 2 a c-a^2-a c a+c & = a c-a^2 a+c = a(c-a) a+c & 1 b-a = a+c -a(a-c) & Now, b-c= 2 a c a+c -c= 2 a c-a c-c^2 a+c & = a c-c^2 a+c = c(a-c) a+c & 1 b-c = a+c c(a-c) & 1 b-a + 1 b-c = a+c -a(a-c) + a+c c(a-c) & = (a+c) (a-c) [- 1 a + 1 c ] & = a+c a c = 1 a + 1 c & = 2 b = 1 b + 1 b = 1 b + 1 2 ( 1 a + 1 c ) aligned Hence, only statement (1) and (2) are correct. Statement (3) is not correct.