Menu Close

if-a-b-c-are-in-H-P-then-prove-that-a-b-c-b-c-a-c-a-b-arw-also-in-H-P-

Tinku Tara 0 Comments
Pin




Question Number 40236 by scientist last updated on 17/Jul/18
if a b c are in H.P then prove that (a/(b+c)),(b/(c+a)),(c/(a+b)) arw also in H.P.
ifabcareinH.Pthenprovethatab+c,bc+a,ca+barwalsoinH.P.
Answered by tanmay.chaudhury50@gmail.com last updated on 17/Jul/18
a,b,c H.P so (1/a),(1/b),(1/c) in A.P (2/b)=(1/a)+(1/c) to prove (a/(b+c)),(b/(c+a)),(c/(a+b)) in H.P if we can prove reciprocal are in A.P ((b+c)/a),((c+a)/b),((a+b)/c) are in A.P now (1/a),(1/b),(1/c) are in A.P multiply a+b+c with each term..results are in A.P ((a+b+c)/a),((a+b+c)/b),((a+b+c)/c) in A.P 1+((b+c)/a),1+((a+c)/b),1+((a+b)/c) inA.P ((b+c)/a),((a+c)/b),((a+b)/c) inA.P (a/(b+c)),(b/(a+c)),(c/(a+b)) are in H.P proved
a,b,cH.Pso1a,1b,1cinA.P2b=1a+1ctoproveab+c,bc+a,ca+binH.PifwecanprovereciprocalareinA.Pb+ca,c+ab,a+bcareinA.Pnow1a,1b,1careinA.Pmultiplya+b+cwitheachterm..resultsareinA.Pa+b+ca,a+b+cb,a+b+ccinA.P1+b+ca,1+a+cb,1+a+bcinA.Pb+ca,a+cb,a+bcinA.Pab+c,ba+c,ca+bareinH.Pproved

Pin

Leave a Reply

Your email address will not be published. Required fields are marked *