Đáp án:
`2+sqrt2>5-sqrt3`
Giải thích các bước giải:
`2+sqrt2`
`sqrt{(2+sqrt2)^2}`
`=sqrt{4+2+4sqrt2}`
`=sqrt{6+4sqrt2}`
`5-sqrt3`
`=sqrt{(5-sqrt3)^2}`
`=sqrt{25+3-10sqrt3}`
`=sqrt{28-10sqrt3}`
`4sqrt2+10sqrt3-22`
`=2(2sqrt2+5sqrt3-11)`
Vì `3>2,89=>sqrt3>1,7`
`=>5sqrt3>8,5`
`2>1,96=>sqrt2>1,4`
`=>2sqrt2>2,8`
`=>2sqrt2+5sqrt3>11`
`=>2(2sqrt2+5sqrt3-11)>0`
`=>4sqrt2+10sqrt3-22>0`
`=>4sqrt2+10sqrt3>22`
`=>4sqrt2>22-10sqrt3`
`=>6+4sqrt2>28-10sqrt3`
`=>2+sqrt2>5-sqrt3`