So sánh căn30 căn29 và căn 29 căn 28

1. Ta có: √2005 + √2003 > √2002 + √2000 1/[√2005 + √2003] < 1/[√2002 + √2000] 2/[√2005 + √2003] < 2/[√2002 + √2000] [2005 - 2003]/[√2005 + √2003] < [2002 - 2000]/[√2002 + √2000] √2005 - √2003 < √2002 - √2000 √2005 + √2000 < √2002 + √2003

1. Tương tự câu a

   √[a + 6] + √[a + 4] > √[a + 2] + √a 1/[√[a + 6] + √[a + 4]] < 1/[√[a + 2] + √a] 2/[√[a + 6] + √[a + 4]] < 2/[√[a + 2] + √a] [[a + 6] - [a + 4]/[√[a + 6] + √[a + 4]] < [[a + 2] - a]/[√[a + 2] + √a] √[a + 6] - √[a + 4] < √[a + 2] - √a √[a + 6] + √a < √[a + 4] + √[a + 2] đúng ko ?

`A=sqrt30-sqrt29`

`B=sqrt29-sqrt28`

Xét `A-B=sqrt30-sqrt29-[sqrt29-sqrt28]`

`=sqrt30-sqrt29-sqrt29+sqrt28`

`=sqrt30-2sqrt29+sqrt28`

Ta có:

`+]` `[sqrt30+sqrt28]^2=30+2sqrt[30*28]+28`

`=58+2sqrt[30*28]=58+2sqrt[[29+1][29-1]]=58+2sqrt[29^2-1]`

`+]` `[2sqrt29]^2=2*2*29=4*29=[2+2]*29`

`=2*29+2*29=58+2sqrt[29^2]`

Vì `29^2-1sqrt[29^2-1]2sqrt[29^2-1]58+2sqrt[29^2-1][sqrt30+sqrt28]^2sqrt30+sqrt28sqrt3-2sqrt29+sqrt28A-BA