`(3/4-x)^3=-8`

`(3/4-x)^3=(-2)^3`

`3/4-x=-2`

`x=3/4-(-2)`

`x=11/4`

\(\dfrac{3}{2}\sqrt{6}+2\sqrt{\dfrac{2}{3}}-4\sqrt{\dfrac{3}{2}}\\ =\sqrt{6.\dfrac{9}{4}}+\sqrt{\dfrac{2}{3}.4}-\sqrt{\dfrac{3}{2}.16}\\ =\sqrt{\dfrac{27}{2}}+\sqrt{\dfrac{8}{3}}-\sqrt{24}\\ =\dfrac{3\sqrt{6}}{2}+\dfrac{2\sqrt{6}}{3}-2\sqrt{6}\\ =\dfrac{3.3\sqrt{6}+2.2\sqrt{6}-6.2\sqrt{6}}{6}=\dfrac{\sqrt{6}}{6}\)

`(x+1)^2-(x-1)^2+3(x+1)(x-1)`

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

`=2x.2+3x^2-3`

`=3x^2+4x-3`

a. `306xx 18-306 xx 8=306 xx (18-8) =306 xx 10=3060`

b. `9 xx 9+25xx9 +33 xx18`

`=9 xx9 + 25 xx 9 + 33 xx 2 xx 9`

`=9x (9+25+33xx2)`

`=9 xx (9+25+66)`

`=9 xx 100`

`=900`

`sin(180^@ -α) = sin180^@ .cosα - cos180^@ .sinα`

`=0.cosα-(-1).sinα=sinα`

a) `x^2+x-6=x^2-2x+3x-6=x(x-2)+3(x-2)=(x-2)(x+3)`

b) `x^2+5x+6=x^2+2x+3x+6=x(x+2)+3(x+2)=(x+2)(x+3)`

c) `x^2-4x+3=x^2-x-3x+3=x(x-1)-3(x-1)=(x-1)(x-3)`

d) `x^2+5x+4=x^2+x+4x+4=x(x+1)+4(x+1)=(x+1)(x+4)`

e) `x^2+3x-10=x^2-2x+5x-10=x(x-2)+5(x-2)=(x-2)(x+5)`

She never stays up late at night.

a) 

`f(x)=3x^2+x+x^4-x^3-x^2+2x+3`

`=x^4-x^3+2x^2+3x+3`

`g(x)=x^4+2x^2+x^3=x^4+x^3+2x^2`

b)

Bậc của `f(x)`: 4

Bậc của `g(x)`: 4

c)

`h(x)=f(x)+g(x)=x^4-x^3+2x^2+3x+3+x^4+x^3+2x^2`

`=2x^4+4x^2+3x+3`

`k(x)=g(x)-f(x)=x^4+x^3+2x^2-(x^4-x^3+2x^2+3x+3)`

`=x^4+x^3+2x^2-x^4+x^3-2x^2-3x-3`

`=2x^3-3x-3`

Áp dụng tính chất của dãy tỉ số bằng nhau:

`x/(0,3)=y/(0,2)=(2z)/1=(z-3x)/(1/2 - 3.0,3) = 1/(-0,4)=-5/2`

`=>x=-5/2 . 0,3 =-3/4`

`y=-5/2 .0,2=-1/2`

`z= -5/2 : 2 =-5/4`

Là `22` và `21`.