Hitung y untuk x+xy+y=2

Pertanyaan

Hitung $y\;$ untuk $x+xy+y=2$

E. Lestari

Master Teacher

Mahasiswa/Alumni Universitas Sebelas Maret

Jawaban terverifikasi

Pembahasan

Dari soal dikaetahui

x plus x y plus y equals 2

Maka

$table attributes columnalign right center left columnspacing 0px end attributes row cell x plus x y plus y end cell equals 2 row cell y plus x y end cell equals cell 2 minus x end cell row cell y open parentheses 1 plus x close parentheses end cell equals cell 2 minus x end cell row y equals cell fraction numerator 2 minus x over denominator 1 plus x end fraction end cell end table$

Sehingga y apostrophe dapat ditentukan dengan cara berikut.

$table attributes columnalign right center left columnspacing 0px end attributes row y equals cell fraction numerator 2 minus x over denominator 1 plus x end fraction end cell row u equals cell 2 minus x rightwards double arrow u apostrophe equals negative 1 end cell row v equals cell 1 plus x rightwards double arrow v apostrophe equals 1 end cell row cell y apostrophe end cell equals cell fraction numerator u apostrophe v minus v apostrophe u over denominator v squared end fraction end cell row blank equals cell fraction numerator negative 1 open parentheses 1 plus x close parentheses minus 1 open parentheses 2 minus x close parentheses over denominator open parentheses 1 plus x close parentheses squared end fraction end cell row blank equals cell fraction numerator negative 1 minus x minus 2 plus x over denominator 1 plus 2 x plus x squared end fraction end cell row blank equals cell fraction numerator negative 3 over denominator x squared plus 2 x plus 1 end fraction end cell end table$

Selanjutnya y double apostrophe dapat ditentukan dengan cara berikut.

$table attributes columnalign right center left columnspacing 0px end attributes row cell y apostrophe end cell equals cell fraction numerator negative 3 over denominator x squared plus 2 x plus 1 end fraction end cell row cell u apostrophe end cell equals cell negative 3 rightwards double arrow u double apostrophe equals 0 end cell row cell v apostrophe end cell equals cell x squared plus 2 x plus 1 rightwards double arrow v double apostrophe equals 2 x plus 2 end cell row cell y apostrophe apostrophe end cell equals cell fraction numerator u double apostrophe v apostrophe minus v double apostrophe u apostrophe over denominator v squared end fraction end cell row blank equals cell fraction numerator 0 minus open parentheses 2 x plus 2 close parentheses open parentheses negative 3 close parentheses over denominator open parentheses x squared plus 2 x plus 1 close parentheses squared end fraction end cell row blank equals cell fraction numerator 6 x minus 6 over denominator open parentheses x squared plus 2 x plus 1 close parentheses squared end fraction end cell end table$

Jadi, nilai y double apostrophe adalah $fraction numerator 6 x minus 6 over denominator open parentheses x squared plus 2 x plus 1 close parentheses squared end fraction$