`b) sqrt{a} + sqrt{b} + sqrt{c} = 3`

`to (sqrt{a} + sqrt{b} + sqrt{c})^2 = 3^2`

`to a + b + c + 2(sqrt{ab} + sqrt{bc} + sqrt{ac}) = 9`

`to 5 + 2(sqrt{ab} + sqrt{bc} + sqrt{ac}) = 9`

`to sqrt{ab} + sqrt{bc} + sqrt{ac} = 2`

Ta có :

`a + 2(sqrt{bc} - 1) = a + 2sqrt{bc} - 2 = a + 2sqrt{bc} - (sqrt{ab} + sqrt{bc} + sqrt{ac})`

` = a + sqrt{bc} - sqrt{ab} - sqrt{ac}`

` = sqrt{a}(sqrt{a} - sqrt{c}) - sqrt{b}(sqrt{a} - sqrt{c})`

` = (sqrt{a} - sqrt{b})(sqrt{a} - sqrt{c})`

Chứng minh tương tự : `b + 2(sqrt{ac} - 1) = (sqrt{b} - sqrt{a})(sqrt{b}-sqrt{c})`

`c + 2(sqrt{ab} - 1) = (sqrt{c}-sqrt{a})(sqrt{c}-sqrt{b})`

`to (sqrt{c} - sqrt{b})/(a + 2(sqrt{bc}-1)) + (sqrt{a}-sqrt{c})/(b+2(sqrt{ac}-1)) + (sqrt{a}-sqrt{b})/(c+2(sqrt{ab}-1))`

` = (sqrt{c}-sqrt{b})/((sqrt{a}-sqrt{b})(sqrt{a}-sqrt{c})) + (sqrt{a}-sqrt{c})/((sqrt{b}-sqrt{a})(sqrt{b}-sqrt{c})) + (sqrt{a} - sqrt{b})/((sqrt{c}-sqrt{a})(sqrt{c}-sqrt{b}))`

` = ( (sqrt{c} - sqrt{b})^2 + (sqrt{a} - sqrt{c})^2 - (sqrt{a} - sqrt{b})^2)/((sqrt{a}-sqrt{b})(sqrt{a}-sqrt{c})(sqrt{c}-sqrt{b}))`

` = (c + b - 2sqrt{bc} + a + c - 2sqrt{ac} - a - b + 2sqrt{ab})/((sqrt{a}-sqrt{b})(sqrt{a}-sqrt{c})(sqrt{c}-sqrt{b}))`

` = (2c - 2sqrt{bc} - 2sqrt{ac} + 2sqrt{ab})/((sqrt{a}-sqrt{b})(sqrt{a}-sqrt{c})(sqrt{c}-sqrt{b}))`

` = ( 2[ sqrt{c}(sqrt{c} - sqrt{a}) - sqrt{b}(sqrt{c} - sqrt{a})])/((sqrt{a}-sqrt{b})(sqrt{a}-sqrt{c})(sqrt{c}-sqrt{b}))`

` = ( 2(sqrt{c} - sqrt{b})(sqrt{c}-sqrt{a}))/((sqrt{a}-sqrt{b})(sqrt{a}-sqrt{c})(sqrt{c}-sqrt{b}))`

` = (-2)/(sqrt{a}-sqrt{b}) = 2/(sqrt{b} - sqrt{a})`

`to đpcm`