Toán

1:

a: x/15=-2/6

=>x/15=-1/3

=>x=-5

b: 3/x=1,8/2

=>3/x=9/10

=>x=3*10/9=30/9=10/3

c: (x-3)/(x+2)=2/7

=>2x+4=7x-21

=>-5x=-25

=>x=5

d: (x+1)/3=(x-6)/8

=>8x+8=3x-18

=>5x=-26

=>x=-26/5

e: (2-x)/5=(x+4)/3

=>3(2-x)=5(x+4)

=>5x+20=6-3x

=>8x=-14

=>x=-7/4

g: (2x+1)/(-3)=(1-x)/2

=>2(2x+1)=3(x-1)

=>4x+2=3x-3

=>x=-5

a: x^3+8=(x+2)(x^2-2x+4)

b: =(3x+1)(9x^2-3x+1)

c: =(x+3)(x^2-3x+9)

d: =(4x-3y)(16x^2+24xy+9y^2)

\(a.x^3+8=\left(x+2\right)\left(x^2-2x+4\right)\) 

\(b.27x^3+1=\left(3x+1\right)\left(9x-3x+1\right)\)

\(c.x^3+27=\left(x+3\right)\left(x^2-3x+9\right)\) 

\(d.64x^3-27y^3=\left(4x-3y\right)\left(16x^2+12xy+9y^2\right)\)  

a: 

b: tọa độ A là;

y=0 và -4/3x-4=0

=>-4/3x=4 và y=0

=>x=-3 và y=0

=>A(-3;0)

=>OA=3

Tọa độ B là:

x=0 và y=-4/3*0-4=-4

=>B(0;-4)

=>OB=4

S OAB=1/2*OA*OB=6(đvdt)

c: tan alpha=-4/3

=>\(\alpha\simeq126^052'\)

\(3C=1+\dfrac{1}{3}+...+\dfrac{1}{3^{98}}\)
=>\(2C=1-\dfrac{1}{3^{99}}\)

=>\(C=\dfrac{1}{2}-\dfrac{1}{2\cdot3^{99}}< \dfrac{1}{2}\)

a: =>4(4x^2-28x+49)-3(4x^2+12x+9)=4x^2-7

=>16x^2-112x+196-12x^2-36x-27=4x^2-7

=>-148x=-176

=>x=44/37

b: =>9x^2-1-4x^2-12x-9=5x^2-5x

=>-12x-10=-5x

=>-7x=10

=>x=-10/7

c: =>(12x-5)^2-(12x+21)^2=7

=>(12x-5-12x-21)(12x-5+12x+21)=7

=>24x+16=-7/26

=>24x=-7/26-16=-423/26

=>x=-141/208

d: =>25x^2+20x+4-9x^2-42x-49-16x^2-128x=8

=>-150x=8-4+49=49-4=45

=>x=-3/10

=>3/4*x=4/5*1/2=2/5

=>x=2/5:3/4=2/5*4/3=8/15

(3/4xX):1/2=4/5

3/4xX=4/5x1/2

3/4xX=2/5

       X=2/5:3/4

       X=8/15

b: =>2x=16/2=8

=>x=4

a: Sửa đề: (3/2)^2x-1=(3/2)^5x-4

=>2x-1=5x-4

=>-3x=-3

=>x=1

9:A>0

=>căn x-1>0

=>x>1

\(B-3=\dfrac{x-\sqrt{x}+1-\sqrt{x}+1}{\sqrt{x}-1}=\dfrac{x+2}{\sqrt{x}-1}\)

\(=\dfrac{x-1+3}{\sqrt{x}-1}\)

\(=\sqrt{x}+1+\dfrac{3}{\sqrt{x}-1}\)

\(=\sqrt{x}-1+\dfrac{3}{\sqrt{x}-1}+2>=2\sqrt{3}+2>0\)

=>B>3

7:

\(A=\dfrac{\left(\sqrt{x}-3\right)^2}{\left(\sqrt{x}-3\right)\left(\sqrt{x}+3\right)}=\dfrac{\sqrt{x}-3}{\sqrt{x}+3}\)

|A|=-A

=>A<=0

=>căn x-3<=0

=>0<=x<9

mà x lớn nhất

nên x=8