Question

if a, b, c are in A. P., prove that a(b+c) /bc, b(c+a) /ca, c(a+b) /ab are also in A. P. ​

Answer 1

Answer:

Step-by-step explanation:

a , b , c are in A.P

//divide by abc

=> a/abc , b/abc, c/abc are in A.P

=> 1/bc, 1/ac, 1/ab are in A.P.

//multiply by ab + bc+ ca

=> ab + bc + ca / bc, ab + bc + ca / ac,  ab + bc + ca / ab are in AP

//subtract 1 from all

=> 1/bc(ab + bc + ca ) - 1 , 1/ac(ab + bc + ca) - 1, 1/ab(ab + bc + ca) - 1 are in A.P

=> ab+bc+ca - bc / bc , ab+bc+ca - ac / ac, ab+bc+ca - ab/ab are in A.P

=> ab + ca /bc , ab + bc/ac, bc + ca / ab are in A.P

=> a(b+c)/bc, b(a+c)/ac, c(a+b)/ab are in A.P