ICSE Class 10 Answered

$begin mathsize 12px style If space straight a space equals space fraction numerator straight b space plus space straight c space over denominator 2 end fraction comma space straight c space equals space fraction numerator straight a space plus space straight b over denominator 2 end fraction space and space straight b space is space the space mean space proportional space between space straight a space and space straight c comma prove space that space 1 over straight a space plus space 1 over straight c space equals space 2 over straight b end style$

Asked by Topperlearning User | 14 Sep, 2017, 09:47: AM

Expert Answer

$Given comma space straight a equals fraction numerator straight b plus straight c over denominator 2 end fraction space and space straight c equals fraction numerator straight a plus straight b over denominator 2 end fraction Since space straight b space is space the space mean space proportional space between space straight a space and space straight c comma space we space have straight b squared equals ac rightwards double arrow straight b squared equals open parentheses fraction numerator straight b plus straight c over denominator 2 end fraction close parentheses open parentheses fraction numerator straight a plus straight b over denominator 2 end fraction close parentheses rightwards double arrow 4 straight b squared equals ab plus straight b squared plus ac plus bc rightwards double arrow 3 straight b squared equals ab plus bc plus ac rightwards double arrow 3 left parenthesis ac right parenthesis equals ab plus bc plus ac rightwards double arrow 2 ac equals ab plus bc rightwards double arrow 2 over straight b equals 1 over straight c plus 1 over straight a space space space space space space space.... left parenthesis Dividing space both space the space sides space by space abc right parenthesis rightwards double arrow 1 over straight a plus 1 over straight c equals 2 over straight b$