`22.`

`-` ĐKXĐ : `{ (x >= 0) , (x != 4) , (x != 1) :}`

`a)P = 1 : [ 1 / (2 + \sqrt{x}) + 2 / (4 - x) - 2 / (4 - 2\sqrt{x}) ] : 1 / (4 - 2\sqrt{x})`

`= 1 : [ (2(2 - \sqrt{x}) + 4 - 2(2 + \sqrt{x})) / (2(4 - x)) ] : 1 / (2(2 - \sqrt{x}))`

`= 1 : [ (4 - 2\sqrt{x} + 4 - 4 - 2\sqrt{x}) / (2(4 - x)) ] : 1 / (2(2 - \sqrt{x}))`

`= 1 : [ (4 - 4\sqrt{x}) / (2(4 - x)) ] : 1 / (2(2 - \sqrt{x}))`

`= 1 : [ (4(1 - \sqrt{x})) / (2(2 - \sqrt{x})(2 + \sqrt{x})) ] . 2(2 - \sqrt{x})`

`= [ (2(2 - \sqrt{x})(2 + \sqrt{x})) / (4(1 - \sqrt{x})) ] . 2(2 - \sqrt{x})`

`= (4(2 - \sqrt{x})^2 (2 + \sqrt{x})) / (4(1 - \sqrt{x}))`

`= ((2 - \sqrt{x})^2 (2 + \sqrt{x})) / (1 - \sqrt{x})`

`b)P = 20`

`-> ((2 - \sqrt{x})^2 (2 + \sqrt{x})) / (1 - \sqrt{x}) = 20`

`-> (4 - 4\sqrt{x} + x)(2 + \sqrt{x}) = 20(1 - \sqrt{x})`

`-> 8 + 4\sqrt{x} - 8\sqrt{x} - 4x + 2x + x\sqrt{x} = 20 - 20\sqrt{x}`

`-> x\sqrt{x} - 2x - 4\sqrt{x} + 8 = 20 - 20\sqrt{x}`

`-> x\sqrt{x} - 2x + 16\sqrt{x} - 12 = 0`

Đặt `t = \sqrt{x}` (với `t >= 0 ^^ t != 2 ^^ t != 1`)

`->t^3 - 2t^2 + 16t - 12 = 0`

Menu 9 2 3 `->t~~0,79783` nên `x~~0,64`

`23.`

`-` ĐKXĐ : `{ (x >= 0) , (y >= 0) , (x != y) :}`a

`a)P = [ (x - y) / (\sqrt{x} - \sqrt{y}) - (\sqrt{x^3} - \sqrt{y^3}) / (x - y) ] : [ ((\sqrt{x} - \sqrt{y})^2 + \sqrt{xy}) / (\sqrt{x} + \sqrt{y}) ]`

`= [ (\sqrt{x} + \sqrt{y}) - ((\sqrt{x} - \sqrt{y})(x + \sqrt{xy} + y)) / ((\sqrt{x} - \sqrt{y})(\sqrt{x} + \sqrt{y})) ] : [ (x - 2\sqrt{xy} + y + \sqrt{xy}) / (\sqrt{x} + \sqrt{y}) ]`

`= [ (\sqrt{x} + \sqrt{y}) - (x + \sqrt{xy} + y) / (\sqrt{x} + \sqrt{y}) ] . [ (\sqrt{x} + \sqrt{y}) / (x - \sqrt{xy} + y) ]`

`= [ ((\sqrt{x} + \sqrt{y})^2 - (x + \sqrt{xy} + y)) / (\sqrt{x} + \sqrt{y}) ] . [ (\sqrt{x} + \sqrt{y}) / (x - \sqrt{xy} + y) ]`

`= (x + 2\sqrt{xy} + y - x - \sqrt{xy} - y) / (x - \sqrt{xy} + y)`

`= \sqrt{xy} / (x - \sqrt{xy} + y)`

`b)` Có `{ (x >= 0) , (y >= 0) :}-> \sqrt{xy} >= 0`

Mặt khác `x - \sqrt{xy} + y = (\sqrt{x} - 1/2 \sqrt{y})^2 + 3/4 y`

Do `x != y` nên `x - \sqrt{xy} + y > 0`

`-> P = \sqrt{xy} / (x - \sqrt{xy} + y) >= 0AAx, y` (đpcm)