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

`-x^3-x^2-x-1=0`

`x^3+x^2+x+1=0`

`(x^3+1)+(x^2+x)=0`

`(x+1)(x^2-x+1)+x(x+1)=0`

`(x+1)(x^2-x+1+x)=0`

`(x+1)(x^2+1)=0`

`[(x+1=0),(x^2+1=0\ (VN)):}`

`x=-1`.

94. `tan(x-15^@)=1`

`<=>x-15^@=45^@+k180^@`

`<=>x=60^@+k180^@`

Có 1 điểm biểu diễn duy nhất:

93.

`sin(2/3 x-π/3)=0`

`<=>2/3 x -π/3+kπ`

`<=> x=π/2 + k (3π)/2\ (k \in ZZ)`

-> Có 3 điểm biểu diễn.

`\sqrt(2-\sqrt3) (\sqrt5 +\sqrt2)`

`=\sqrt(5(2-\sqrt3)) + \sqrt(2(2-\sqrt3))`

`=\sqrt(10-5\sqrt3)+\sqrt(4-2\sqrt3)`

`(x+4/5)(x-2/3)=0`
`[(x+4/5=0),(x-2/3=0):}`
`[(x=-4/5),(x=2/3):}`

`=>` A.

`4x^3 y (-2x^2y^3)(-xy^3)`

`=[4.(-2).(-1)].(x^3 .x^2 .x).(y.y^3 .y^3)`

`=8x^6y^7`

a)

\(A=\left(\dfrac{\sqrt{x}}{2}-\dfrac{1}{2\sqrt{x}}\right).\left(\dfrac{x-\sqrt{x}}{\sqrt{x}+1}-\dfrac{x+\sqrt{x}}{\sqrt{x}-1}\right)\\ =\dfrac{x-1}{2\sqrt{x}}.\left(\dfrac{\sqrt{x}\left(\sqrt{x}-1\right)}{\sqrt{x}+1}-\dfrac{\sqrt{x}\left(\sqrt{x}+1\right)}{\sqrt{x}-1}\right)\\ =\dfrac{\left(\sqrt{x}+1\right)\left(\sqrt{x}-1\right)}{2\sqrt{x}}.\dfrac{\sqrt{x}\left(\sqrt{x}-1\right)^2-\sqrt{x}\left(\sqrt{x}+1\right)^2}{\left(\sqrt{x}+1\right)\left(\sqrt{x}-1\right)}\\ =\dfrac{\sqrt{x}\left(\sqrt{x}-1+\sqrt{x}+1\right)\left(\sqrt{x}-1-\sqrt{x}-1\right)}{2\sqrt{x}}\\ =\dfrac{\sqrt{x}.2\sqrt{x}.\left(-2\right)}{2\sqrt{x}}=-2\sqrt{x}\)

b)

 \(A< -4\Leftrightarrow-2\sqrt{x}< -4\\ \Leftrightarrow\sqrt{x}>2\\ \Leftrightarrow x>4\)

`(x+2)(x^2-2x+4)-x^2 .(x-2) -2x^2`

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

`=x^3+8-x^3+2x^2-2x^2`

`=8`

`(m^2+m)cos2x=m^2-m-3-m^2 cos2x`

`<=> (2m^2+m)cos2x=m^2-m-3`

`<=>cos2x =(m^2-m-3)/(2m^2+m)`

PT có nghiệm `<=> -1 <= (m^2-m-3)/(2m^2+m) <=1`

`<=> [(m<=-1 \vee m>=1),(-1/2 < m <0):}`

`M=64+32+16.4=160` đvC