`1.`

`a.`

        `48^2 + 52^2 + 96.52`

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

`=(48+52)^2`

`=100^2`

`=10000`

`b.`

        `198(198-196)+98^2`

`=198^2 - 198.196+98^2`

`= 198^2 - 2.198 . 98+98^2`

`=(198-98)^2`

`=100^2`

`=10000`

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`2.`

`a.`

        `(2x-1)^2+(4x+1)(x-3)+7x`

`=4x^2-4x+1` `+` `4x^2-12x+x-3` `+` `7x`

`=(4x^2+4x^2)-(4x+12x-x-7x)+(1-3)`

`=8x^2-8x-2`

`b.`

        `(x+3y)^2-x(x+6)+9(y-1)(y+1)`

`=x^2+6xy+9y^2` `-` `x^2-6x+ 9(y^2-1)`

`=6xy+9y^2-6x+9y^2+9`

`=18y^2+6xy-6x+9`

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`3.`

`a.`

        `(16x-2)(x+1)-(4x-3)^2=5`

`⇔(16x^2+16x-2x-2)-(16x^2-24x+9)=5`

`⇔16x^2+14x-2-16x^2+24x-9=5`

`⇔38x-11=5`

`⇔38x=16`

`⇔x=8/19`

Vậy `x=8/19`

`b.`

        `(x+8)^2+2(x+8)+1=9x^2`

`⇔(x+8+1)^2=(3x)^2`

`⇔(x+9)^2-(3x)^2=0`

`⇔(x+9-3x)(x+9+3x)=0`

`⇔(9-2x)(4x+9)=0`

`⇔ [(9-2x=0),(4x+9=0):}`

`⇔ [(x=9/2),(x=-9/4):}`

Vậy `S={9/2;-9/4}`

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`4.`

        `4x^2-12x+5045`

`=[(2x)^2-2.2x.3+9]-9+5045`

`=(2x-3)^2+5036`

Thay `x=103/2` vào biểu thức, ta được:

         `(103/2 .2-3)^2+5036`

`= (103-3)^2+5036`

`=100^2+5036`

`=10000+5036`

`=15036`

Vậy giá trị của biểu thức là `15036` tại `x=103/2`

`#` `ccUh`