Bài 3: Nhân, chia số hữu tỉ

`(x+1)/3  = 9/(x+1)^2`

`(x+1)^3 = 3*9=27`

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

`x+1=3`

`x=3-1=2`

Vậy `x=2`

\(< =>\left(x+1\right)\cdot\left(x+1\right)^2=9\cdot3< =>\left(x+1\right)^3=27< =>x+1=3< =>x=2\)

`a, 2x(x-1/2) = 2x^2 - x`.

`b, 11/12 - (2/5 + x) = 2/3`

`11/12 - 2/5 - x = 2/3`

`31/60 - x = 2/3`

`x = 11/60`

`c, 3^x . 9 = 3 . 9^x`.

`-> x = 1`.

`d, 2^(3x+2) = 4^(x+5)`

`2^(3x+2)= 2^(2x+10)`

`x = 8`

Bạn cần giúp bài nào thì bạn nên ghi chú rõ ra.

\(1.\)

\(b,\left(4.2^5\right)\div\left(2^3.\dfrac{1}{16}\right)=\left(2^2.2^5\right)\div\dfrac{1}{2}=2^7\div\dfrac{1}{2}=2^7.2=2^8\)

\(2.\)

\(b,\left(-\dfrac{1}{3}\right).x=\dfrac{1}{81}\)

\(x=\dfrac{1}{81}\div\left(-\dfrac{1}{3}\right)\)

\(x=-\dfrac{1}{27}\)

\(c,\left(2x-3\right)^2=16\)

\(\left(2x-3\right)^2=4^2\)

\(2x=4+3\)

\(2x=7\)

\(x=7\div2\)

\(x=\dfrac{7}{2}\)

\(3.\)

\(a,\left(\dfrac{2}{3}x-\dfrac{1}{3}\right)^5=\dfrac{1}{243}\)

\(\left(\dfrac{2}{3}x-\dfrac{1}{3}^5\right)=\left(\dfrac{1}{3}\right)^5\)

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

\(\dfrac{2}{3}x=\dfrac{2}{3}\)

\(x=\dfrac{2}{3}\div\dfrac{2}{3}\)

\(x=1\)

\(b,\left(\dfrac{2}{5}-3x\right)^2=\dfrac{9}{25}\)

\(\left(\dfrac{2}{5}-3x\right)^2=\left(\dfrac{3}{5}\right)^2\)

\(3x=\dfrac{2}{5}-\dfrac{3}{5}\)

\(3x=\dfrac{-1}{5}\)

\(x=-\dfrac{1}{5}\div3\)

\(x=-\dfrac{1}{15}\)

\(c,\left(x-\dfrac{3}{5}\right)^2=4\)

\(\left(x-\dfrac{3}{5}\right)^2=2^2\)

\(x=2+\dfrac{3}{5}\)

\(x=\dfrac{13}{5}\)

Bài 43

a) \(\left(x-2\right)^2=1\)

\(\left(x-2\right)^2=1^2\) hoặc \(\left(x-2\right)^2=\left(-1\right)^2\)

\(x-2=1;x-2=-1\)

*) x - 2 = 1

x = 1 + 2

x = 3

*) x - 2 = -1

x = -1 + 2

x = 1

Vậy x = 1; x = 3

b) \(\left(2x-1\right)^3=27\)

\(\left(2x-1\right)^3=3^3\)

\(2x-1=3\)

\(2x=3+1\)

\(2x=4\)

\(x=\dfrac{4}{2}\)

\(x=2\)

c) \(\left(x+\dfrac{1}{2}\right)^2=\dfrac{1}{4}\)

\(\left(x+\dfrac{1}{2}\right)^2=\left(\dfrac{1}{2}\right)^2;\left(x+\dfrac{1}{2}\right)^2=\left(-\dfrac{1}{2}\right)^2\)

\(x+\dfrac{1}{2}=\dfrac{1}{2};x+\dfrac{1}{2}=-\dfrac{1}{2}\)

*) \(x+\dfrac{1}{2}=\dfrac{1}{2}\)

\(x=0\)

*) \(x+\dfrac{1}{2}=-\dfrac{1}{2}\)

\(x=-\dfrac{1}{2}-\dfrac{1}{2}\)

\(x=-1\)

Vậy \(x=-1\); \(x=0\)

d) \(\left(2x+3\right)^2=\dfrac{9}{121}\)

\(\left(2x+3\right)^2=\left(\dfrac{3}{11}\right)^2;\left(2x+3\right)^2=\left(-\dfrac{3}{11}\right)^2\)

\(2x+3=\dfrac{3}{11};2x+3=-\dfrac{3}{11}\)

*) \(2x+3=\dfrac{3}{11}\)

\(2x=\dfrac{3}{11}-3\)

\(2x=-\dfrac{30}{11}\)

\(x=-\dfrac{30}{11}:2\)

\(x=-\dfrac{15}{11}\)

*) \(2x+3=-\dfrac{3}{11}\)

\(2x=-\dfrac{3}{11}-3\)

\(2x=-\dfrac{36}{11}\)

\(x=-\dfrac{36}{11}:2\)

\(x=-\dfrac{18}{11}\)

Vậy \(x=-\dfrac{18}{11};x=-\dfrac{15}{11}\)

e) \(\left(3x-1\right)^3=-\dfrac{8}{27}\)

\(\left(3x-1\right)^3=\left(-\dfrac{2}{3}\right)^3\)

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

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

\(3x=\dfrac{1}{3}\)

\(x=\dfrac{1}{3}:3\)

\(x=\dfrac{1}{9}\)

Bài 44

a) \(x:\left(-\dfrac{1}{2}\right)^3=-\dfrac{1}{2}\)

\(x=\left(-\dfrac{1}{2}\right).\left(-\dfrac{1}{2}\right)^3\)

\(x=\left(-\dfrac{1}{2}\right)^4\)

\(x=\dfrac{1}{16}\)

b) \(\left(\dfrac{3}{4}\right)^5.x=\left(\dfrac{3}{4}\right)^7\)

\(x=\left(\dfrac{3}{4}\right)^7:\left(\dfrac{3}{4}\right)^5\)

\(x=\left(\dfrac{3}{4}\right)^2\)

\(x=\dfrac{9}{16}\)

c) \(\left(x^4\right)^2=\dfrac{x^{12}}{x^5}\)

\(x^8=x^7\)

\(x^8-x^7=0\)

\(x^7.\left(x-1\right)=0\)

\(x^7=0;x-1=0\)

*) \(x^7=0\)

x = 0

*) x - 1 = 0

x = 1

Vậy x = 0; x = 1

Bài 2:

a)

\(\dfrac{-25}{28}\)x\(\dfrac{21}{100}\)

=\(\dfrac{-525}{2800}\)=\(\dfrac{-3}{16}\)

b)

\(\dfrac{7}{9}\):\(\dfrac{-35}{12}\)

=\(\dfrac{7}{9}\)x\(\dfrac{-12}{35}\)

=\(\dfrac{-84}{315}\)=\(\dfrac{-4}{15}\)

Làm những bài nào vậy cậu?

`= (50+0,9)(50-0,9) - (50+0,8)(50-0,8)`

`= 50^2 - 0,9^2 - 50^2 + 0,8^2`

`= -0,81 +0,64`

`= -0,17`

Chụp tách ra bn!

\(=\dfrac{1.3\left(1-2\right)}{2.6}-\dfrac{5}{12}=\dfrac{-1}{2}-\dfrac{5}{12}=\dfrac{-11}{12}\)

`C=1/(-2021) -1/(-2019) +1/(-2019) -1/(-2017) +...+1/(-3) -1/(-1)`

`C=(-1)/2021 +1=2022/2021`