Bài 1:

a: \(\left(\frac{9}{25}-2^2\right):\left(-0,2\right)\)

\(=\left(\frac{9}{25}-4\right):\left(\frac{-1}{5}\right)=\frac{-91}{25}\cdot\frac{-5}{1}=\frac{91}{5}\)

b: \(\left(-\frac15\right)^2+\frac15-2\cdot\left(-\frac12\right)^3-\frac12\)

\(=\frac{1}{25}+\frac15-2\cdot\frac{-1}{8}-\frac12\)

\(=\frac{1}{25}+\frac{5}{25}+\frac14-\frac12=\frac{6}{25}-\frac14=\frac{24}{100}-\frac{25}{100}=-\frac{1}{100}\)

c: \(\left(3-\frac14+\frac23\right)^2:2022^0\)

\(=\left(\frac{36}{12}-\frac{3}{12}+\frac{8}{12}\right)^2=\left(\frac{41}{12}\right)^2=\frac{1681}{144}\)

d: \(2^2\cdot9:\left(3\frac45+0,2\right)\)

\(=4\cdot9:\left(3,8+0,2\right)\)

\(=\frac{36}{4}=9\)

e: \(\left(\frac14+\frac23\right)^2-1\frac13=\left(\frac{3}{12}+\frac{8}{12}\right)^2-\frac43\)

\(=\left(\frac{11}{12}\right)^2-\frac43=\frac{121}{144}-\frac{192}{144}=-\frac{71}{144}\)

f: \(1:\left(-1\frac52+0,5\right)^2\)

\(=1:\left(-\frac72+\frac12\right)^2\)

\(=1:\left(-3\right)^2=\frac19\)

Bài 2:

a: \(-\frac{5}{14}+\frac38-\frac{2}{14}-\frac38+\frac12\)

\(=\left(-\frac{5}{14}-\frac{2}{14}+\frac12\right)+\left(\frac38-\frac38\right)\)

\(=\left(-\frac{7}{14}+\frac{7}{14}\right)+0=0+0=0\)

b: \(\frac{7}{15}-\frac57+\frac{23}{15}+\frac57-\frac35\)

\(=\left(\frac{7}{15}+\frac{23}{15}\right)-\frac35+\left(\frac57-\frac57\right)\)

\(=\frac{30}{15}-\frac35=2-\frac35=\frac75\)

c: \(-\frac25\cdot\frac57+\frac{-2}{5}\cdot\frac97\)

\(=-\frac25\left(\frac57+\frac97\right)=-\frac25\cdot2=-\frac45\)

d: \(\frac{55}{27}+\frac{-21}{5}+\frac{-55}{27}-\frac{-21}{5}\)

\(=\left(\frac{55}{27}-\frac{55}{27}\right)+\left(-\frac{21}{5}+\frac{21}{5}\right)\)

=0+0=0

e: \(\frac57:\left(\frac{15}{8}-\frac14\right)-\frac57:\left(\frac14+\frac12\right)\)

\(=\frac57:\left(\frac{15}{8}-\frac28\right)-\frac57:\left(\frac14+\frac24\right)\)

\(=\frac57:\frac{13}{8}-\frac57:\frac34\)

\(=\frac57\cdot\frac{8}{13}-\frac57\cdot\frac43=\frac57\left(\frac{8}{13}-\frac43\right)=\frac57\cdot\left(\frac{24}{39}-\frac{52}{39}\right)\)

\(=\frac57\cdot\frac{-28}{39}=\frac{5\cdot\left(-4\right)}{39}=-\frac{20}{39}\)

f: \(16\frac27:\left(-\frac35\right)-28\frac27:\left(-\frac35\right)\)

\(=\left(16+\frac27\right)\cdot\frac{-5}{3}-\left(28+\frac27\right)\cdot\frac{-5}{3}\)

\(=-\frac53\left(16+\frac27-28-\frac27\right)=-\frac53\cdot\left(-12\right)=20\)

Bài 1:

a: \(\left(\frac{9}{25}-2^2\right):\left(-0,2\right)\)

\(=\left(\frac{9}{25}-4\right):\left(\frac{-1}{5}\right)=\frac{-91}{25}\cdot\frac{-5}{1}=\frac{91}{5}\)

b: \(\left(-\frac15\right)^2+\frac15-2\cdot\left(-\frac12\right)^3-\frac12\)

\(=\frac{1}{25}+\frac15-2\cdot\frac{-1}{8}-\frac12\)

\(=\frac{1}{25}+\frac{5}{25}+\frac14-\frac12=\frac{6}{25}-\frac14=\frac{24}{100}-\frac{25}{100}=-\frac{1}{100}\)

c: \(\left(3-\frac14+\frac23\right)^2:2022^0\)

\(=\left(\frac{36}{12}-\frac{3}{12}+\frac{8}{12}\right)^2=\left(\frac{41}{12}\right)^2=\frac{1681}{144}\)

d: \(2^2\cdot9:\left(3\frac45+0,2\right)\)

\(=4\cdot9:\left(3,8+0,2\right)\)

\(=\frac{36}{4}=9\)

e: \(\left(\frac14+\frac23\right)^2-1\frac13=\left(\frac{3}{12}+\frac{8}{12}\right)^2-\frac43\)

\(=\left(\frac{11}{12}\right)^2-\frac43=\frac{121}{144}-\frac{192}{144}=-\frac{71}{144}\)

f: \(1:\left(-1\frac52+0,5\right)^2\)

\(=1:\left(-\frac72+\frac12\right)^2\)

\(=1:\left(-3\right)^2=\frac19\)

Bài 2:

a: \(-\frac{5}{14}+\frac38-\frac{2}{14}-\frac38+\frac12\)

\(=\left(-\frac{5}{14}-\frac{2}{14}+\frac12\right)+\left(\frac38-\frac38\right)\)

\(=\left(-\frac{7}{14}+\frac{7}{14}\right)+0=0+0=0\)

b: \(\frac{7}{15}-\frac57+\frac{23}{15}+\frac57-\frac35\)

\(=\left(\frac{7}{15}+\frac{23}{15}\right)-\frac35+\left(\frac57-\frac57\right)\)

\(=\frac{30}{15}-\frac35=2-\frac35=\frac75\)

c: \(-\frac25\cdot\frac57+\frac{-2}{5}\cdot\frac97\)

\(=-\frac25\left(\frac57+\frac97\right)=-\frac25\cdot2=-\frac45\)

d: \(\frac{55}{27}+\frac{-21}{5}+\frac{-55}{27}-\frac{-21}{5}\)

\(=\left(\frac{55}{27}-\frac{55}{27}\right)+\left(-\frac{21}{5}+\frac{21}{5}\right)\)

=0+0=0

e: \(\frac57:\left(\frac{15}{8}-\frac14\right)-\frac57:\left(\frac14+\frac12\right)\)

\(=\frac57:\left(\frac{15}{8}-\frac28\right)-\frac57:\left(\frac14+\frac24\right)\)

\(=\frac57:\frac{13}{8}-\frac57:\frac34\)

\(=\frac57\cdot\frac{8}{13}-\frac57\cdot\frac43=\frac57\left(\frac{8}{13}-\frac43\right)=\frac57\cdot\left(\frac{24}{39}-\frac{52}{39}\right)\)

\(=\frac57\cdot\frac{-28}{39}=\frac{5\cdot\left(-4\right)}{39}=-\frac{20}{39}\)

f: \(16\frac27:\left(-\frac35\right)-28\frac27:\left(-\frac35\right)\)

\(=\left(16+\frac27\right)\cdot\frac{-5}{3}-\left(28+\frac27\right)\cdot\frac{-5}{3}\)

\(=-\frac53\left(16+\frac27-28-\frac27\right)=-\frac53\cdot\left(-12\right)=20\)

1-x = (1/3 ) mũ 2
1-x = +-1/3
1-x =1/3
x=0,6
1-x=-1/3
x=1,3

Ta có: \(\left(1-x\right)^2=\frac19\)

=>\(\left(x-1\right)^2=\frac19\)

=>\(\left[\begin{array}{l}x-1=\frac13\\ x-1=-\frac13\end{array}\right.\Rightarrow\left[\begin{array}{l}x=\frac13+1=\frac43\\ x=-\frac13+1=\frac23\end{array}\right.\)

a: |3x-5|+|2x+3|=7(1)

TH1: \(x<-\frac32\)

=>2x+3<0; 3x-5<0

(1) sẽ trở thành: \(-2x-3-3x+5=7\)

=>-5x+2=7

=>-5x=5

=>x=-1(loại)

TH2: \(-\frac32\le x<\frac53\)

=>2x+3>=0; 3x-5<0

(1) sẽ trở thành: 2x+3-3x+5=7

=>8-x=7

=>x=1(nhận)

TH3: \(x\ge\frac53\)

=>2x+3>0; 3x-5>=0

(1) sẽ trở thành: 2x+3+3x-5=7

=>5x-2=7

=>5x=9

=>\(x=\frac95\) (nhận)

b: |x|+|x+2|=3(2)

TH1: x<-2

=>x+2<0; x<0

(2) sẽ trở thành: -x-2-x=3

=>-2x=5

=>\(x=-\frac52\) (nhận)

TH2: -2<=x<0

=>x+2>=0; x<0

(2) sẽ trở thành x+2-x=3

=>2=3(vô lý)

TH3: x>=0

=>x+2>0; x>=0

(2) sẽ trở thành: x+2+x=3

=>2x+2=3

=>2x=1

=>\(x=\frac12\) (nhận)

c: |3x-5|=|x+2|

=>\(\left[\begin{array}{l}3x-5=x+2\\ 3x-5=-x-2\end{array}\right.\Rightarrow\left[\begin{array}{l}2x=7\\ 4x=3\end{array}\right.\Rightarrow\left[\begin{array}{l}x=\frac72\\ x=\frac34\end{array}\right.\)

= (37,5.6,5 + 3,5.37,5) – (7,5.3,4 + 6,6.7,5)

= 37,5(6,5 + 3,5) – 7,5(3,4 + 6,6)

= 37,5.10 – 7,5.10

= 375 – 75 = 300

= ( 37,5 . 6,5 + 3,5 . 37,5 ) – ( 7,5 . 3,4 + 6,6 . 7,5 )

= 37,5 . ( 6,5 + 3,5 ) – 7,5 ( 3,4 + 6,6 )

= 37,5 . 10 – 7,5 . 10

= 375 – 75

= 300

x+1/x= 1 + 1/x

để x+1/x là một số nguyên => 1/x là số nguyên => x thuộc ước của 1=> x = 1; -1

Ta có :

(x+3)^4=4*(x+3)^3

hay (x+3)^4-4*(x+3)^3=0

(x+3)^3*(x+3−4)=0

(x+3)^3*(x−1)=0

TH1: x+3=0⇒x=−3

TH2: x−1=0⇒x=1

Vậy x=-3 hoặc x=1

(3+x)^4 = 4*(x+3)^3

(3+x)^3 * [(3+x) - 4] = 0

(3+x)^3 * (x - 1) = 0

x = -3 hoặc x = 1

\(\left(\frac17\right)^{x+1}\) \(=\frac{1}{49}\)

\(\left(\frac17\right)^{x+1}\) \(=\left(\frac17\right)^2\)

\(x+1=2\)

\(x=2-1\)

\(x=1\)

LMV gamer ơi, cậu thông minh thế

\(\frac{-30}{17}:\frac{-15}{-34}\)

\(=-\frac{30}{17}:\frac{15}{34}\)

\(=-\frac{30}{17}\cdot\frac{34}{15}=-\frac{34}{17}\cdot\frac{30}{15}=-2\cdot2=-4\)

\(\frac{-30}{17}:\frac{-15}{-34}\)

\(=\frac{-30}{17}:\frac{15}{34}\)

\(=\frac{-30}{17}.\frac{34}{15}\)

\(=\frac{-1020}{255}\)

\(=-4\)

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