`( x - 1)^3 = 1/8`

` ( x - 1)^3 = ( 1/2)^3`

` x - 1 = 1/2`

`x = 1/2 + 2/2`

`x = 3/2`

`\sqrt{x + 4\sqrt{x} + 4} = 5x + 2 (x >= 0)`

`<=> \sqrt{(\sqrt{x} + 2)^2} = 5x + 2`

`<=> |\sqrt{x} + 2| = 5x + 2`

`<=> \sqrt{x} + 2 = 5x + 2`

`<=> \sqrt{x} - 5x = 0`

`<=> \sqrt{x}(1 - 5\sqrt{x}) = 0`

`<=> \sqrt{x} = 0` hoặc `1 - 5\sqrt{x} = 0`

`<=> x = 0` hoặc `\sqrt{x} = 1/5`

`<=> x = 0(`tm`)` hoặc `x = 1/25(`tm`)`

Vậy `S = {0 ; 1/25}`

`(1/3)^(x + 3) + (1/3)^(x + 2) = 4/27`

`=> (1/3)^(x + 2 + 1) + (1/3)^(x + 2) = 4/27`

`=> (1/3)^(x + 2) . 1/3 + (1/3)^(x + 2) = 4/27`

`=> (1/3)^(x + 2) . (1/3 + 1) = 4/27`

`=> (1/3)^(x + 2) . 4/3 = 4/27`

`=> (1/3)^(x + 2) = 4/27 : 4/3 = 1/9 = (1/3)^2`

`=> x +2 =2`

`=> x = 0`

Vậy `x = 0`

`a)`

`C = (3x + \sqrt{9x} - 3)/(x + \sqrt{x} - 2) - (\sqrt{x}+1)/(\sqrt{x} + 2) - (\sqrt{x} - 2)/(\sqrt{x} - 1)`

`(x >= 0 ; x` $\neq$ `1)`

`C = (3x + 3\sqrt{x} - 3)/((\sqrt{x} - 1)(\sqrt{x} + 2)) - ((\sqrt{x} + 1)(\sqrt{x} - 1))/((\sqrt{x}- 1)(\sqrt{x} + 2)) - ((\sqrt{x} - 2)(\sqrt{x} + 2))/((\sqrt{x} - 1)(\sqrt{x} + 2))`

`C = (3x + 3\sqrt{x} - 3 - x + 1 - x + 4)/((\sqrt{x} - 1)(\sqrt{x} + 2))`

`C = (3x + 3\sqrt{x} - 2x + 2)/((\sqrt{x} - 1)(\sqrt{x} + 2))`

`C = (x + 3\sqrt{x} + 2)/((\sqrt{x} - 1)(\sqrt{x} + 2))`

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

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

`b)`

`x = 3 + 2\sqrt{2} = 2 + 2\sqrt{2} + 1 = (\sqrt{2} + 1)^2`

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

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

`C = (\sqrt{2} + 2)/(\sqrt{2})`

`C = 1 + \sqrt{2}`

`B = (4/(x - 5) + (3x - 1)/(x^2 - 25) - 1/(x + 5)) . (x^2 + 5x)/(x + 4)`

`B = [(4(x + 5))/((x - 5)(x + 5)) + (3x - 1)/((x - 5)(x + 5)) - (x - 5)/((x - 5)(x + 5))] . (x^2 + 5x)/(x + 4)`

`B = (4x + 20 + 3x - 1 - x + 5)/((x - 5)(x + 5)) . (x(x + 5))/(x + 4)`

`B = (6x+24)/((x - 5)(x + 5)) . (x(x + 5))/(x + 4)`

`B = (6(x + 4))/((x - 5)(x + 5)) . (x(x + 5))/(x + 4)`

`B = (6x)/(x - 5)`

`T = \sqrt{2+\sqrt{3}} . \sqrt{2+\sqrt{2+\sqrt{3}}} . \sqrt{2 - \sqrt{2+\sqrt{3}}}`

`T = \sqrt{2+\sqrt{3}} . \sqrt{(2+\sqrt{2+\sqrt{3}})(2 - \sqrt{2} + \sqrt{3})}`

`T = \sqrt{2+\sqrt{3}} . \sqrt{4 - (2 + \sqrt{3})^2}`

`T = \sqrt{2+\sqrt{3}} . \sqrt{4 - |2 + \sqrt{3}|}`

`T = \sqrt{2 + \sqrt{3}} . \sqrt{4 - 2 - \sqrt{3}}`

`T = \sqrt{2 + \sqrt{3}} . \sqrt{2 - \sqrt{3}}`

`T = \sqrt{(2 + \sqrt{3})(2 - \sqrt{3})}`

`T = \sqrt{4 - 3}`

`T = \sqrt{1} = 1`

Ta có: 

`(a - b)^2 + (b - c)^2 + (c - a)^2 >= 0` với mọi `a;b;c`

`=> a^2 - 2ab + b^2 + b^2 - 2bc + c^2 + c^2 - 2ca + a^2 >= 0`

`=> 2(a^2+b^2+c^2)>=2ab+2bc+2ca`

`=> 2(a^2+b^2+c^2)+(a^2+b^2+c^2)>=2ab+2bc+2ca+(a^2+b^2+c^2)`

`=> 3(a^2+b^2+c^2)>=(a+b+c)^2`

`=> đpcm`

`(sin2x-sinx)/(1-cosx+cos2x)`

`=(2sinxcosx-sinx)/(1-cosx+2cos^2x-1)`

`= (2sinxcosx-sinx)/(2cos^2x-cosx)`

`=(sinx( 2cosx-1))/(cosx(2cosx-1) )`

`=(sinx)/(cosx) . (2cosx-1)/(2cosx-1)`

`= tan x . 1`

` => m = 1`

`sin4xcot2x-cos4x`

`=2sin2xcos2x . (cos2x)/(sin2x)  - (2cos^2 2x-1)`

`=2cos^2 2x - 2cos^2 2x+1`

`= 1`