Selesaikan setiap pertidaksamaan irasional satu variabel berikut. 5t−5t2+6≥2

Pertanyaan

Selesaikan setiap pertidaksamaan irasional satu variabel berikut.

$5t-5\sqrt{t^2+6}\geq2$

I. Sutiawan

Master Teacher

Mahasiswa/Alumni Universitas Pasundan

Jawaban terverifikasi

Jawaban

pertidaksamaan 5 t minus 5 square root of t squared plus 6 end root greater or equal than 2

tidak memiliki penyelesaian.

Pembahasan

Syarat:

table attributes columnalign right center left columnspacing 0px end attributes row cell t squared plus 6 end cell greater or equal than 0 row cell negative infinity end cell less than cell t less than infinity space..... space left parenthesis 1 right parenthesis end cell end table

Untuk menyelesaikan pertidaksamaan 5 t minus 5 square root of t squared plus 6 end root greater or equal than 2 kita pindahkan bentuk akar ke ruas yang lain kemudian kuadratkan kedua ruas, sehingga:

$table attributes columnalign right center left columnspacing 0px end attributes row cell 5 t minus 5 square root of t squared plus 6 end root end cell greater or equal than 2 row cell 5 t end cell greater or equal than cell 5 square root of t squared plus 6 end root plus 2 end cell row cell open parentheses 5 t close parentheses squared end cell greater or equal than cell open parentheses 5 square root of t squared plus 6 end root plus 2 close parentheses squared end cell row cell 25 t squared end cell greater or equal than cell 25 left parenthesis t squared plus 6 right parenthesis plus 20 square root of t squared plus 6 end root plus 4 end cell row cell 25 t squared end cell greater or equal than cell 25 t squared plus 150 plus 20 square root of t squared plus 6 end root plus 4 end cell row cell 25 t squared minus 25 t squared minus 150 minus 4 end cell greater or equal than cell 20 square root of t squared plus 6 end root end cell row cell negative 154 end cell greater or equal than cell 20 square root of t squared plus 6 end root end cell row cell 20 square root of t squared plus 6 end root end cell less or equal than cell negative 154 end cell row cell square root of t squared plus 6 end root end cell less or equal than cell negative 154 over 20 end cell row cell square root of t squared plus 6 end root end cell less or equal than cell fraction numerator negative 77 over denominator 10 end fraction end cell row t equals cell ϕ space.... space left parenthesis 2 right parenthesis end cell end table$

Iriskan (1) dan (2) sehingga penyelesaian menjadi table attributes columnalign right center left columnspacing 0px end attributes row blank blank t end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank ϕ end table atau tidak ada nilai yangmemenuhi pertidaksamaan tersebut.

Jadi, pertidaksamaan tidak memiliki penyelesaian.