1: 90<x<180

=>cosx<0

=>\(cosx=-\sqrt{1-\left(\dfrac{4}{5}\right)^2}=-\dfrac{3}{5}\)

\(sin2x=2\cdot sinx\cdot cosx=2\cdot\dfrac{4}{5}\cdot\dfrac{-3}{5}=\dfrac{-24}{25}\)

\(cos2x=2\cdot cos^2x-1=2\cdot\dfrac{9}{25}-1=-\dfrac{7}{25}\)

\(tan2x=\dfrac{-24}{25}:\dfrac{-7}{25}=\dfrac{24}{7}\)

2: 0<x<90

=>cosx>0

=>\(cosx=\sqrt{1-\left(\dfrac{1}{2}\right)^2}=\dfrac{\sqrt{3}}{2}\)

\(cos2x=2\cdot cos^2x-1=2\cdot\dfrac{3}{4}-1=\dfrac{6}{4}-1=\dfrac{2}{4}=\dfrac{1}{2}\)

5^x.5^x+1.5^x+2<100.................00:2²⁴

                      Có 24 số 0

5^3x.5¹.5²<10^24:22²⁴

5^3x.5³<5²⁴

5^3x<5²⁴:5³

5^3x<5²¹

=>3x=21

     x=21:3

     x=7\(\in\)N

Vậy x=7

Chúc bn học tốt

a) \(\frac{2}{3}x-\frac{2}{5}=\frac{1}{2}x-\frac{1}{3}\)

=> \(\frac{2}{3}x-\frac{2}{5}-\frac{1}{2}x+\frac{1}{3}=0\)

=> \(\left(\frac{2}{3}x-\frac{1}{2}x\right)+\left(-\frac{2}{5}+\frac{1}{3}\right)=0\)

=> \(\frac{1}{6}x-\frac{1}{15}=0\Rightarrow\frac{1}{6}x=\frac{1}{15}\Rightarrow x=\frac{1}{15}:\frac{1}{6}=\frac{1}{15}\cdot6=\frac{2}{5}\)

Vậy x = 2/5

b) \(\frac{1}{3}x+\frac{2}{5}\left(x+1\right)=0\)

=> \(\frac{1}{3}x+\frac{2}{5}x+\frac{2}{5}=0\)

=> \(\frac{11}{15}x+\frac{2}{5}=0\Rightarrow\frac{11}{15}x=-\frac{2}{5}\)

=> \(x=\left(-\frac{2}{5}\right):\frac{11}{15}=\left(-\frac{2}{5}\right)\cdot\frac{15}{11}=-\frac{6}{11}\)

Vậy x = -6/11

c) \(\frac{2}{3}-\frac{1}{3}\left(x-\frac{3}{2}\right)-\frac{1}{2}\left(2x+1\right)=5\)

=> \(\frac{2}{3}-\frac{1}{3}x+\frac{1}{2}-x-\frac{1}{2}=5\)

=> \(\left(\frac{2}{3}+\frac{1}{2}-\frac{1}{2}\right)+\left(-\frac{1}{3}x-x\right)=5\)

=> \(\frac{2}{3}-\frac{4}{3}x=5\)

=> \(\frac{4}{3}x=-\frac{13}{3}\Rightarrow x=\left(-\frac{13}{3}\right):\frac{4}{3}=\left(-\frac{13}{3}\right)\cdot\frac{3}{4}=-\frac{13}{4}\)

Vậy x = -13/4

d) \(\frac{11}{5}-\left(\frac{7}{9}-x\right)\cdot\frac{3}{8}=\frac{61}{90}+\frac{x}{3}\)

=> \(\frac{11}{5}-\frac{3}{8}\left(\frac{7}{9}-x\right)=\frac{61}{90}+\frac{30x}{90}\)

=> \(\frac{11}{5}-\frac{7}{24}+\frac{3}{8}x=\frac{61+30x}{90}\)

=> \(\frac{229}{120}+\frac{3}{8}x=\frac{61+30x}{90}\)

=> \(\frac{229}{120}+\frac{3x}{8}=\frac{61+30x}{90}\)

=> \(\frac{229}{120}+\frac{45x}{120}=\frac{61+30x}{90}\)

=> \(\frac{229+45x}{120}=\frac{61+30x}{90}\)

=> \(\frac{3\left(229+45x\right)}{360}=\frac{4\left(61+30x\right)}{360}\)

=> \(3\left(229+45x\right)=4\left(61+30x\right)\)

=> \(687+135x=244+120x\)

=> \(687+135x-244-120x=0\)

=> \(\left(687-244\right)+\left(135x-120x\right)=0\)

=> \(443+15x=0\)

=> \(15x=-443\Rightarrow x=-\frac{443}{15}\)

Vậy x = -443/15

câu a là phân số ak

a) quá dài

b)<=>x^2+2x+1=90

=>x^2+2x-89=0

áp dụng denta

=>2^2-(-4(1.89))=360

\(\Rightarrow x_{1,2}=\frac{-b+-\sqrt{\Delta}}{2a}=\frac{-2+-\sqrt{360}}{2}\)

=>x=\(+-3\sqrt{10}-1\)

HỎI CÂU KHÓ THẾ AI MÀ TRẢ LỜI ĐƯỢC

Mk trả lời đc nè nguyen hung son :))

A = 1 . 2 + 2 . 3 + 3 . 4 + 4 . 5 + ... + 90 . 100

3A = 1 . 2 . 3 + 2 . 3 . ( 4 - 1 ) + 3 . 4 . ( 5 - 2 ) + .... + 90 . 100 . ( 101 - 98 )

3A = 1 . 2 . 3 + 2 . 3 . 4 - 1 + 3 . 4 . 5 - 2 + ... + 90 . 100 . 101 - 98

3A = 99 . 100 . 101

A = ( 99 . 100 . 101 ) : 3

A = 999900 : 3

A = 333300

Vậy A = 333300

minh dang ding tra loi the dau tay a

duong k cho ban ay luon di

câu 1 

=> x+1/2+x+1/3+x+1/4-x-1/5-x-1/6=0

=> (x+x+x-x-x)+(1/2+1/3+1/4-1/5-1/6)=0

=> x+43/60=0

=> x = -43/60

câu dưới làm tương tự bạn nhé!

  Trả lời :

( X + 1 ) + ( X + 2 ) + ( X + 3 ) + ( X + 4 ) + ( X + 5 ) = 90

=> ( X + X + X + X + X ) + ( 1 + 2 + 3 + 4 + 5 )         = 90

=> ( X x 5 ) + 15                                                        = 90

=> X x 5                                                                     = 90 - 15

=> X x 5                                                                     = 75

=> X                                                                           = 75 : 5

=> X                                                                           = 15.

 Vậy X = 15.

   Học tốt nha~

X + (1+2+3+4+5) = 90

X+ 15                = 90

X                      = 90-15

X                      = 75

Ta có ( X+1) + (X+2) + ( X+3) + ( X+4) + ( X+5)=90

      <=> X+1+X+2+X+3+X+4+X+5 = 90

      <=> ( X+X+X+X+X) + ( 1+2+3+4+5) = 90

       <=> 5X + 15 =90

        <=> 5X= 90 -15= 75

        <=> X = 75:5

          <=> X= 15

Vậy X =15 

nhớ tích cho mk nha :>