Himpunan penyelesaian √x^2-3x+2<_√x+7 adalah...

Himpunan penyelesaian √x^2-3x+2<_√x+7 adalah…

Jawab:

Penjelasan dengan langkah-langkah:

$sqrt{x^2-3x+2}leq sqrt{x+7}~~~~~~~~~~~...kuadratkan~kedua~ruas\\x^2-3x+2leq x+7\\x^2-4x-5leq 0\\(x-5)(x+1)leq 0\\-1leq x leq 5~~~~~~~...(i)\\\syarat~yang~harus~dipenuhi~:\\x^2-3x+2geq 0\\(x-1)(x-2)geq 0\\xleq 1~~atau~~xgeq 2~~~~~~~~...(ii)\\\x+7geq 0\\xgeq -7~~~~~~~~~~~~~...(iii)\\\HPnya~adalah~irisan~(i)~(ii)~dan~(iii)\\HP:-1leq xleq 1~~atau~~2leq xleq 5$