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CBSE Class 11-science Answered

If a be the AM and x, y be the two GM's between b and c, show that x^3+y^3=2abc.
Asked by shaktidevgun | 14 Jan, 2016, 03:49: PM
answered-by-expert Expert Answer
begin mathsize 14px style Given space straight a equals straight A. straight M. space between space straight b space and space straight c rightwards double arrow straight a equals fraction numerator straight b plus straight c over denominator 2 end fraction Since space straight x space and space straight y space are space two space straight G. straight M. space between space straight b space and space straight c comma straight b comma straight x comma straight y space are space in space straight G. straight P. rightwards double arrow straight x equals br comma space straight y equals br squared comma space straight c equals br cubed where space straight r space is space the space common space ratio space of space straight G. straight P. Now comma space straight x cubed plus straight y cubed equals left parenthesis br right parenthesis cubed plus open parentheses br squared close parentheses cubed equals straight b cubed straight r cubed open parentheses 1 plus straight r cubed close parentheses equals straight b cubed cross times straight c over straight b open parentheses 1 plus straight c over straight b close parentheses equals straight b squared straight c open parentheses fraction numerator straight b plus straight c over denominator straight b end fraction close parentheses equals bc open parentheses straight b plus straight c close parentheses equals bc left parenthesis 2 straight a right parenthesis equals 2 abc rightwards double arrow straight x cubed plus straight y cubed equals 2 abc end style
Answered by Rashmi Khot | 15 Jan, 2016, 09:59: AM

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