`#3107.101107`

`2.`

`a)`

`3/4 \div (x + 1/2) - 5/6 = -(1/2)^2`

`=> 3/4 \div (x + 1/2) = -1/4 + 5/6`

`=> 3/4 \div (x + 1/2) = 7/12`

`=> x + 1/2 = 3/4 \dvi 7/12`

`=> x + 1/2 = 9/7`

`=> x = 9/7 - 1/2`

`=> x = 11/14`

Vậy, `x = 11/14`

`b)`

\(\left(-\dfrac{1}{3}\right)^{x-3}=\dfrac{1}{81}\\ \Rightarrow\left(-\dfrac{1}{3}\right)^{x-3}=\left(-\dfrac{1}{3}\right)^4\\ \Rightarrow x-3=4\\ \Rightarrow x=4+3\\ \Rightarrow x=7\)

`c)`

\(\left(2x-3\right)^2-\dfrac{1}{4}=6^{20}\div6^{19}\\ \Rightarrow\left(2x-3\right)^2-\dfrac{1}{4}=6\\ \Rightarrow\left(2x-3\right)^2=6+\dfrac{1}{4}\\ \Rightarrow\left(2x-3\right)^2=\dfrac{25}{4}\\ \Rightarrow\left(2x-3\right)^2=\left(\pm\dfrac{5}{2}\right)^2\\ \Rightarrow\left[{}\begin{matrix}2x-3=\dfrac{5}{2}\\2x-3=-\dfrac{5}{2}\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}2x=\dfrac{5}{2}+3\\2x=-\dfrac{5}{2}+3\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}2x=\dfrac{11}{2}\\2x=\dfrac{1}{2}\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x=\dfrac{11}{4}\\x=\dfrac{1}{4}\end{matrix}\right.\)

Vậy, `x \in {11/4; 1/4}`

`d)`

\(\dfrac{x+1}{2022}+\dfrac{x+3}{2020}+\dfrac{x+5}{2018}+\dfrac{x+7}{2016}+4=0\)

`=> ((x + 1)/2022 + 1) + ((x + 3)/2020 + 1) + ((x + 5)/2018 + 1) + ((x + 7)/2016 + 1) = 0`

`=> (x + 1 + 2022)/2022 + (x + 3 + 2020)/2020 + (x + 5 + 2018)/2018 + (x + 7 + 2016)/2016 = 0`

`=> (x + 2023)/2022 + (x + 2023)/2020 + (x + 2023)/2018 + (x + 2023)/2016 = 0`

`=> (x + 2023)(1/2022 + 1/2020 + 1/2018 + 1/2016) = 0`

Vì `1/2022 + 1/2020 + 1/2018 + 1/2016 \ne 0`

`=> x + 2023 = 0`

`=> x = -2023`

Vậy, `x = -2023.`

`#3107.101107`

`a)`

\(\dfrac{-4}{3}+\dfrac{2}{3}\div x=\dfrac{-2}{5}\\ \Rightarrow\dfrac{2}{3}\div x=-\dfrac{2}{5}+\dfrac{4}{3}\\ \Rightarrow\dfrac{2}{3}\div x=\dfrac{14}{15}\\ \Rightarrow x=\dfrac{2}{3}\div\dfrac{14}{15}\\ \Rightarrow x=\dfrac{5}{7}\)

Vậy, `x = 5/7`

`b)`

\(\dfrac{7}{3}-1\dfrac{3}{5}\cdot x=-1\dfrac{2}{3}\)

$\Rightarrow$ `1 3/5 * x = 7/3 - (-1 2/3)`

$\Rightarrow$`1 3/5 * x = 7/3 + 5/3`

$\Rightarrow$`8/5 * x = 12/3`

$\Rightarrow$`x = 4 \div 8/5`

$\Rightarrow$`x = 5/2`

Vậy, `x = 5/2`

`c)`

\(\dfrac{-3}{5}\cdot x-\left(x+2,5\right)=\dfrac{-13}{15}\)

$\Rightarrow$`-3/5x - x - 2,5 = -13/15`

$\Rightarrow$`-8/5x = -13/15 + 2,5`

$\Rightarrow$`-8/5x = 49/30`

$\Rightarrow$`x = 49/30 \div (-8/5)`

$\Rightarrow$`x = -49/48`

Vậy, `x = -49/48.`

=)) Em đi học cũng toàn đi muộn không à, may là lúc nào cũng kịp sát giờ vô lớp, nhưng có điều mấy bạn cờ đỏ không tha:))

Sử dụng HĐT:

\(A^2-B^2=\left(A-B\right)\left(A+B\right)\)

Hoặc bạn dùng cách này cho bài a) cũng được

\(\left(A-B\right)^2=A^2-2AB+B^2\\ \left(A+B\right)^2=A^2+2AB+B^2.\)

`#3107.101107`

`2.`

`a)`

`(x - 5)^2 - (x + 5)^2`

`= (x - 5 - x - 5)(x - 5 + x + 5)`

`= -10 * 2x`

`= -20x`

`b)`

\(\left(6x+1\right)\left(1-6x\right)+36x^2-5\)

`= -(6x + 1)(6x - 1) + 36x^2 - 5`

`= -(36x^2 - 1) + 36x^2 - 5`

`= -36x^2 + 1 + 36x^2 - 5`

`= -4`