Question

Help me

Answer 1

`4)`

`a)48^2+52^2+96.52`

`=48^2+2.48.52+52^2`

`=(48+52)^2=100^2=10000`

`b)[2022^2-1]/[2022^2+2023]`

`=[(2022-1)(2022+1)]/[2022^2+(2022+1)]`

`=[(2022-1).(2022+1)]/[2022(2022+1)]`

`=[2022-1]/2022=2021/2022`

 

`5)`

`a)A=x^2-2x+5=x^2-2x+1+4=(x-1)^2+4`

Vì `(x-1)^2 >= 0 AA x<=>(x-1)^2+4 >= 4 AA x`

 Dấu "`=`" xảy ra `<=>(x-1)^2=0<=>x=1`

`b)B=x^2-4xy+5y^2-6y+2x+5`

`B=x^2-4xy+4y^2+y^2-2y+1-4y+2x+5`

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

`B=(x-2y)^2+2(x-2y)+1+(y-1)^2+4`

`B=(x-2y+1)^2+(y-1)^2+4`

Vì `(x-2y+1)^2 >= 0 AA x,y` mà `(y-1)^2 >= 0 AA y`

 `=>(x-2y+1)^2+(y-1)^2 >= 0 AA x,y`

`<=>(x-2y+1)^2+(y-1)^2+4 >= 4 AA x,y`

 Hay `B >= 4 AA x,y`

Dấu "`=`" xảy ra `<=>{(x-2y+1=0),(y-1=0):}<=>{(y=1),(x=1):}`