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Carilah nilai x positif yang memenuhi  persamaan berikut. xxxx...​​​​=4x+4x+4x+4x+...​​​​

Pertanyaan

Carilah nilai undefined positif yang memenuhi  persamaan berikut.

begin mathsize 14px style square root of x square root of x square root of x square root of x... end root end root end root end root equals square root of 4 x plus square root of 4 x plus square root of 4 x plus square root of 4 x plus... end root end root end root end root end style  

  1. begin mathsize 14px style... end style  

  2. begin mathsize 14px style... end style  

A. Armanda

Master Teacher

Mahasiswa/Alumni Universitas Indraprasta PGRI

Jawaban terverifikasi

Jawaban

 nilai undefined positif yang memenuhi  persamaan berikut adalah begin mathsize 14px style x equals 5 end style.

Pembahasan

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell square root of x square root of x square root of x square root of x... end root end root end root end root end cell equals p row cell square root of x open parentheses square root of x square root of x square root of x square root of x... end root end root end root end root close parentheses end cell equals p row cell open parentheses square root of x open parentheses square root of x square root of x square root of x square root of x... end root end root end root end root close parentheses close parentheses squared end cell equals cell p squared end cell row cell x times left parenthesis square root of x square root of x square root of x square root of x... end root end root end root end root right parenthesis end cell equals cell space p squared end cell row cell x times p end cell equals cell p squared end cell row cell x p minus p squared end cell equals 0 row cell p left parenthesis x minus p right parenthesis end cell equals 0 row p equals cell 0 space atau space x equals p space... space left parenthesis straight i right parenthesis end cell end table end style 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell square root of 4 x plus square root of 4 x plus square root of 4 x plus square root of 4 x plus... end root end root end root end root end cell equals p row cell square root of 4 x end root plus open parentheses square root of 4 x plus square root of 4 x plus square root of 4 x plus square root of 4 x plus... end root end root end root end root close parentheses end cell equals p row cell open parentheses square root of 4 x end root plus open parentheses square root of 4 x plus square root of 4 x plus square root of 4 x plus square root of 4 x plus... end root end root end root end root close parentheses close parentheses end cell equals cell p squared end cell row cell 4 x plus square root of 4 x plus square root of 4 x plus square root of 4 x plus square root of 4 x plus... end root end root end root end root end cell equals cell p squared end cell row cell 4 x plus p end cell equals cell p squared end cell row cell 4 x end cell equals cell p squared minus p space... space left parenthesis ii right parenthesis end cell end table end style 

Subsitusikan begin mathsize 14px style x equals p end style pada persamaan table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell size 14px left parenthesis size 14px ii size 14px right parenthesis end cell end table.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell 4 x end cell equals cell p squared minus p end cell row cell p squared minus p minus 4 x end cell equals 0 row cell p squared minus p minus 4 p end cell equals 0 row cell p squared minus 5 p end cell equals 0 row cell p left parenthesis p minus 5 right parenthesis end cell equals 0 row p equals cell 0 space atau space p equals 5 end cell row blank blank blank end table end style 

Pada persamaan begin mathsize 14px style left parenthesis straight i right parenthesis end styleundefined maka begin mathsize 14px style x equals 0 space atau space x equals 5 end style.

Jadi, nilai undefined positif yang memenuhi  persamaan berikut adalah begin mathsize 14px style x equals 5 end style.

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