rõ ràng x,y>0" role="presentation" style="display: inline; line-height: normal; font-size: 13px; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; color: rgb(25, 43, 64); font-family: helvetica, arial, verdana, tahoma, sans-serif; background-color: rgb(255, 255, 255); position: relative;">x,y>0x,y>0 vì nếu x,y≤0" role="presentation" style="display: inline; line-height: normal; font-size: 13px; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; color: rgb(25, 43, 64); font-family: helvetica, arial, verdana, tahoma, sans-serif; background-color: rgb(255, 255, 255); position: relative;">x,y≤0x,y≤0 thì 2x+4y≤2" role="presentation" style="display: inline; line-height: normal; font-size: 13px; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; color: rgb(25, 43, 64); font-family: helvetica, arial, verdana, tahoma, sans-serif; background-color: rgb(255, 255, 255); position: relative;">2x+4y≤22x+4y≤2
áp dụng AM-GM ta có:
32=2x+4y≥22x+2y" role="presentation" style="display: inline; line-height: normal; font-size: 13px; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; color: rgb(25, 43, 64); font-family: helvetica, arial, verdana, tahoma, sans-serif; background-color: rgb(255, 255, 255); position: relative;">32=2x+4y≥22x+2y−−−−√32=2x+4y≥22x+2y
⇔x+2y≤8" role="presentation" style="display: inline; line-height: normal; font-size: 13px; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; color: rgb(25, 43, 64); font-family: helvetica, arial, verdana, tahoma, sans-serif; background-color: rgb(255, 255, 255); position: relative;">⇔x+2y≤8⇔x+2y≤8
lại tiếp tục với AM-GM:
8≥x+2y≥22xy" role="presentation" style="display: inline; line-height: normal; font-size: 13px; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; color: rgb(25, 43, 64); font-family: helvetica, arial, verdana, tahoma, sans-serif; background-color: rgb(255, 255, 255); position: relative;">8≥x+2y≥22xy−−−√8≥x+2y≥22xy
⇒xy≤8" role="presentation" style="display: inline; line-height: normal; font-size: 13px; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; color: rgb(25, 43, 64); font-family: helvetica, arial, verdana, tahoma, sans-serif; background-color: rgb(255, 255, 255); position: relative;">⇒xy≤8⇒xy≤8
vậy dấu bằng phải xảy ra khi x=4;y=2" role="presentation" style="display: inline; line-height: normal; font-size: 13px; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; color: rgb(25, 43, 64); font-family: helvetica, arial, verdana, tahoma, sans-serif; background-color: rgb(255, 255, 255); position: relative;">x=4;y=2
[TẶNG BẠN] TRỌN BỘ Bí kíp học tốt 08 môn
