`1/3+5/3:x=1/2`

`5/3:x=1/2-1/3`

`5/3:x=1/6`

`x=5/3:1/6`

`x=10`

vậy `x=10`

`A=1+2+2^2+2^3+....+2^2021`

`2A=2+2^2+2^3+....+2^2022`

`=>2A-A=A=2^2022-1`

`P=(2^{10}.3^8+5.4^{5}.3^8)/(2^{10}.27^3-2^10.9^4)`

`P=(2^{10}.3^8+5.2^{10}.3^8)/(2^{10}.3^9-2^{10}.3^8)`

`P=(2^{10}.3^8(1+5))/(2^{10}.3^8(3-1))`

`P=(1+5)/(3-1)=6/2=3`

`P=(2^{10}.3^8+5.4^{5}.3^8)/(2^{10}.27^3-2^10.9^4)`

`P=(2^{10}.3^8+5.2^{10}.3^8)/(2^{10}.3^9-2^{10}.3^8)`

`P=(2^{10}.3^8(1+5))/(2^{10}.3^8(3-1))`

`P=(1+5)/(3-1)=6/2=3`

`a)2023^2023(7^10:7^8-3.2^4-2^2023:2^2023)`

`=2023^2023(7^2-3.2^4-1)`

`=2023^2023(49-48-1)`

`=0`

`b)(2^100+2^101+2^102):(2^97+2^98+2^99)`

`=2^3(2^97+2^98+2^99):(2^97+2^98+2^99)`

`=2^3=8`

`51/57=(3.17)/(3.19)=17/19`

`1717/1919=(101.17)/(101.19)=17/19`

`171717/191919=(10101.17)/(10101.19)=17/19`

`=>51/57=1717/1919=171717/191919`

`1/(-27)=(1/(-x))^3`

`(1/(-3))^3=(1/(-x))^3`

`-3=-x`

`x=3`

Vậy `x=3`

`A=1/3-(x+1)^2`

Vì `(x+1)^2>=0`

`=>1/3-(x+1)^2<=1/3-0=1/3`

Hay `A<=1/3`

Dấu "=" xảy ra khi `x+1=0<=>x=-1`

Vậy `max_A=1/3<=>x=-1`

`(3-x)^3=-27/64`

`(3-x)^3=(-3/4)^3`

`3-x=-3/4`

`x=3+3/4`

`x=15/4`

Vậy `x=15/4`

`A=-4+(x-3)^2`

Vì `(x-3)^2>=0=>A>=-4`

Dấu "=" xảy ra khi `x=3`

vậy `min_A=-4<=>x=3`

`B=1/2-(5x+1)^2`

Vì `(5x+1)^2>=0`

`=>1/2-(5x+1)^2<=1/2`

Dấu "=" xảy ra khi `5x+1=0<=>x=-1/5`

vậy `max_B=1/2<=>x=-1/5`