\(1,P=\dfrac{x^3+y^3}{x^2-xy+y^2}\cdot\dfrac{x+y}{x^2-y^2}\\ =\dfrac{\left(x+y\right)\left(x^2-xy+y^2\right)}{x^2-xy+y^2}\cdot\dfrac{x+y}{\left(x+y\right)\left(x-y\right)}\\ =\dfrac{x+y}{x-y}\)

2, Ta có:

\(x=\sqrt{7-4\sqrt{3}}=\sqrt{\left(2-\sqrt{3}\right)^2}=2-\sqrt{3}\\ y=\sqrt{4-2\sqrt{3}}=\sqrt{\left(\sqrt{3}-1\right)^2}=\sqrt{3}-1\\ \Rightarrow P=\dfrac{2-\sqrt{3}+\sqrt{3}-1}{2-\sqrt{3}-\sqrt{3}+1}\\ =\dfrac{1}{3-2\sqrt{3}}=\dfrac{3+2\sqrt{3}}{-3}\)

\(A=\dfrac{1}{2+\sqrt{x}}+\dfrac{1}{2-\sqrt{x}}-\dfrac{2\sqrt{x}}{4-x}\\ =\dfrac{2-\sqrt{x}}{\left(2+\sqrt{x}\right)\left(2-\sqrt{x}\right)}+\dfrac{2+\sqrt{x}}{\left(2-\sqrt{x}\right)\left(2+\sqrt{x}\right)}-\dfrac{2\sqrt{x}}{\left(2-\sqrt{x}\right)\left(2+\sqrt{x}\right)}\\ =\dfrac{2-\sqrt{x}+2+\sqrt{x}-2\sqrt{x}}{\left(2-\sqrt{x}\right)\left(2+\sqrt{x}\right)}\\ =\dfrac{4-2\sqrt{x}}{\left(2-\sqrt{x}\right)\left(2+\sqrt{x}\right)}\\ =\dfrac{2\left(2-\sqrt{x}\right)}{\left(2-\sqrt{x}\right)\left(2+\sqrt{x}\right)}\\ =\dfrac{2}{2+\sqrt{x}}\\ A=\dfrac{1}{3}\Rightarrow\dfrac{2}{2+\sqrt{x}}=\dfrac{1}{3}\Rightarrow\sqrt{x}+2=6\\ \Rightarrow\sqrt{x}=4\Leftrightarrow x=16\left(tm\right)\)

\(1,ĐK:a\ge0;a\ne4\)

\(C=\dfrac{a}{a-16}-\dfrac{2}{\sqrt{a}-4}-\dfrac{2}{\sqrt{a}+4}\\ =\dfrac{a}{\left(\sqrt{a}-4\right)\left(\sqrt{a}+4\right)}-\dfrac{2\left(\sqrt{a}+4\right)}{\left(\sqrt{a}-4\right)\left(\sqrt{a}+4\right)}-\dfrac{2\left(\sqrt{a}-4\right)}{\left(\sqrt{a}-4\right)\left(\sqrt{a}+4\right)}\\ =\dfrac{a-2\sqrt{a}-8-2\sqrt{a}+8}{\left(\sqrt{a}-4\right)\left(\sqrt{a}+4\right)}\\ =\dfrac{a-4\sqrt{a}}{\left(\sqrt{a}-4\right)\left(\sqrt{a}+4\right)}\\ =\dfrac{\sqrt{a}\left(\sqrt{a}-4\right)}{\left(\sqrt{a}-4\right)\left(\sqrt{a}+4\right)}\\ =\dfrac{\sqrt{a}}{\sqrt{a}+4}\)

\(2,a=9-4\sqrt{5}=\left(\sqrt{5}-2\right)^2\\ \Rightarrow C=\dfrac{\sqrt{\left(\sqrt{5}-2\right)^2}}{\sqrt{\left(\sqrt{5}-2\right)^2}+4}\\ =\dfrac{\sqrt{5}-2}{\sqrt{5}-2+4}\\ =\dfrac{\sqrt{5}-2}{\sqrt{5}+2}=9-4\sqrt{5}\)

B10:

`a)x^2-3x=0`

`<=>x(x-3)=0`

`<=>x=0` hoặc `x=3`

`b,(x^3-4x^2)-(x-4)=0`

`<=>x^2(x-4)-(x-4)=0`

`<=>(x^2-1)(x-4)=0`

`<=>(x-1)(x+1)(x-4)=0`

`<=>x=1` hoặc `x=-1` hoặc `x=4`

`c)(4x^2-25)-9(2x-5)^2=0`

`<=>(2x-5)(2x+5)-9(2x-5)^2=0`

`<=>(2x-5)[2x+5-9(2x-5)]=0`

`<=>(2x-5)(2x+5-18x+45)=0`

`<=>(2x-5)(50-16x)=0`

`<=>2x=5` hoặc `16x=50`

`<=>x=5/2` hoặc `x=25/8`

`(-3/2)^2+1/2*(4,5-2)`

`=9/4+1/2*(2,5)`

`=9/4+1/2*(5/2)`

`=9/4+5/4`

`=(9+5)/4)`

`=14/4`

`=7/2`

`d)-6t+9t^2=0`

`<=>9t^2-6t=0`

`<=>3t(3t-2)=0`

`<=>3t=0` hoặc `3t-2=0`

`<=>t=0` hoặc `t=2/3`

`h)-t=3t^2`

`<=>3t^2+t=0`

`<=>t(3t+1)=0`

`<=>t=0` hoặc `3t+1=0`

`<=>t=0` hoặc `t=-1/3`

`l)2t^3=3t^2`

`<=>2t^3-3t^2=0`

`<=>t^2(2t-3)=0`

`<=>t^2=0` hoặc `2t-3=0`

`<=>t=0` hoặc `t=3/2`

`p)27t^2-54t^3=0`

`<=>54t^3-27t^2=0`

`<=>27t^2(3t-1)=0`

`<=>27t^2=0` hoặc `3t-1=0`

`<=>t=0` hoặc `t=1/3` 

`a)x^3=1`

`<=>x^3=1^3`

`<=>x=1`

`b)x^3=8`

`<=>x^3=2^3`

`<=>x=2`

`c)x^3=27`

`<=>x^3=3^3`

`<=>x=3`

`d)x^3=64`

`<=>x^3=4^3`

`<=>x=4`

`e)x^3=125`

`<=>x^3=5^3`

`<=>x=5`

`f)x^3=-1`

`<=>x^3=(-1)^3`

`<=>x=-1`

`g)x^3=-8`

`<=>x^3=(-2)^3`

`<=>x=-2`

`h)x^3=-27`

`<=>x^3=(-3)^3`

`<=>x=-3`

`i)(-x)^3=-64`

`<=>(-x)^3=(-4)^3`

`<=>-x=-4`

`<=>x=4`

`j)(-x)^3=-125`

`<=>(-x)^3=(-5)^3`

`<=>-x=-5`

`<=>x=5`

`k)(-x)^3=-216`

`<=>(-x)^3=(-6)^3`

`<=>-x=-6`

`<=>x=6`

`l)(-x)^3=-343`

`<=>(-x)^3=(-7)^3`

`<=>-x=-7`

`<=>x=7` 

`a)36xy^3-12x^2y^2`

`=12xy^2*3y-12xy^2*x`

`=12xy^2*(3y-x)`

`b)x^2-x+1/4`

`=x^2-2*x*1/2+(1/2)^2`

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

`c)a^2x+a^2y-7x-7y`

`=a^2(x+y)-7(x+y)`

`=(a^2-7)(x+y)` 

`d)3x^2y-9xy^2+12x^2y^2`

`=3xy*x-3xy*3y+3xy*4xy`

`=3xy(x-3y+4xy)` 

`e)x^3-6x^2y+12xy^2-8y^3`

`=x^3-3*x^2*2y+3*x*(2y)^2-(2y)^3`

`=(x-2y)^3` 

\(1,\sqrt{18x}\cdot\sqrt{8x}\\ =\sqrt{18x\cdot8x}\\ =\sqrt{144x^2}\\ =\left|12x\right|\\ =12x\left(x>0\right)\\ 2,\sqrt{6y}\cdot\sqrt{24y}\\ =\sqrt{6y\cdot24y}\\ =\sqrt{144y^2}\\ =\left|12y\right|\\ =-12y\left(y\le0\right)\\ 3,\sqrt{75\left(x-18\right)^2}\\ =\sqrt{\left[5\sqrt{3}\left(x-18\right)\right]^2}\\ =\left|5\sqrt{3}\left(x-18\right)\right|\\ =5\sqrt{3}\left(x-18\right)\left(x>18\right)\) 

`B=x^3-y^2+x+x^2y-2x^2+2021+3y-xy`

`=(x^3+x^2y)+(-xy-y^2)+x+3y-2x^2+2021`

`=x^2(x+y)-y(x+y)+x+3y-2x^2+2021`

`=2x^2-2y+x+3y-2x^2+2021`

`=(2x^2-2x^2)+x+(3y-2y)+2021`

`=x+y+2021`

`=2+2021`

`=2023`