Trả lời:

5, x² - y² + 4x + 4 

= ( x² + 4x + 4 ) - y²

= ( x + 2 )² - y²

= ( x + 2 - y ) ( x + 2 + y )

6, x² + 2x - 4y² - 4y

= ( x² - 4y² ) + ( 2x - 4y )

= ( x - 2y ) ( x + 2y ) + 2 ( x - 2y )

= ( x - 2y ) ( x + 2y + 2 )

7, 3x² - 4y + 4x - 3y²

= ( 3x² - 3y² ) + ( 4x - 4y )

= 3 ( x² - y² ) + 4 ( x - y )

= 3 ( x - y ) ( x + y ) + 4 ( x - y )

= ( x - y ) [ 3 ( x + y ) + 4 ]

= ( x - y ) ( 3x + 3y + 4 )

8, x⁴ - 6x³ + 54x - 81

= ( x⁴ - 81 ) - ( 6x³ - 54x )

= ( x² - 9 ) ( x² + 9 ) - 6x ( x² - 9 )

= ( x² - 9 ) ( x² + 9 - 6x )

= ( x - 3 ) ( x + 3 ) ( x - 3 )²

= ( x - 3 )³ ( x + 3 )

a, \(x^2-y^2+4x+4=\left(x+2\right)^2-y^2=\left(x+2-y\right)\left(x+2+y\right)\)

b, \(x^2+2x-4y^2-4y=\left(x-2y\right)\left(x+2y\right)+2\left(x-2y\right)=\left(x-2y\right)\left(x+2+2y\right)\)

c, \(3x^2-4y+4x-3y^2=3\left(x-y\right)\left(x+y\right)-4\left(y-x\right)=\left(x-y\right)\left(3x+3y+4\right)\)

d, \(x^4-6x^3+54x-81=\left(x^2+9\right)\left(x-3\right)\left(x+3\right)-6x\left(x^2-9\right)\)

\(=\left(x-3\right)\left(x+3\right)\left(x^2-6x+9\right)=\left(x-3\right)^3\left(x+3\right)\)

5, x²-y²+4x+4

=(x²+4x+4)-y²

=(x+2)²-y²

=(x+2-y)(x+2+y)

6, x²+2x-4y²-4y

=(x²-4y²)+(2x-4y)

=(x-2y)(x+2y)+2(x-2y)

=(x-2y)(x+2y+2)

7, 3x²-4y+4x-3y²

=(3x²-3y²)+(4x-4y)

=3(x²-y²)+4(x-y)

=3(x-y)(x+y)+4(x-y)

=(x-y)[3(x+y)+4]

=(x-y)(3x+3y+4)

8, x⁴-6x³+54x-81

=(x⁴-81)-(6x³-54x)

=(x²-9)(x²+9)-6x(x²-9)

=(x²-9)(x²+9-6x)

=(x+3)(x-3)(x-3)²

=(x+3)(x-3)³

#H

54x 10 = 540

54x100 = 5400

54x1000 = 540 00

108x10 = 1080

108x100 = 10800

108x1000 = 108000

690x10 = 6900

690x100 = 69000

690x1000 = 690 000

54 x 10 = 540

54 x 100 = 5400

54 x 1000 =  54000

108 x 10 = 1080

108 x 100 = 10800

108 x 1000 = 108000

690 x 10 = 6900

690 x 100 = 69000

690  x 1000 = 690000

`54xx 10 = 540`

`54xx100 = 5400`

`54xx1000 = 540 00`

`108xx10 = 1080`

`108xx100 = 10800`

`108xx1000 = 108000`

`690xx10 = 6900`

`690xx100 = 69000`

`690xx1000 = 690 000`

mik toàn thấy ":(" thôi:)

0,8 : (54x 1,25 + ( 108% -252) :31)
=0,8 : (67.5 + ( -250,92) :31)
=0,8 : ( 67.5 -250,92 :31)
=0,8 : ( 67.5 -8.09)
=0,8:59.41
=0.0134

\(\left\{{}\begin{matrix}2x+y=5\\4x-y=7\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}4x+2y=10\\4x-y=7\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}2x+y=5\\\left(4x-4x\right)+\left(2y+y\right)=10-7\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}2x+y=5\\3y=3\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}2x+y=5\\y=1\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}2x+1=5\\y=1\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}2x=4\\y=1\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}x=2\\y=1\end{matrix}\right.\)

Vậy hệ pt có nghiệm duy nhất \(\left(x;y\right)=\left(2;1\right)\)

b: \(9x^2+54+81=\left(3x+9\right)^2\)

c: \(=\left(y-\dfrac{1}{2}\right)^2\)

d: \(=\left(4x^3-3\right)^2\)

Lấy lôgarit theo cơ số 5 hai vế của bất phương trình, ta được:

Chọn C

\(2x+5=54\Leftrightarrow2x=49x=\dfrac{49}{2}\)

\(x\times2+5=54\)

\(x\times2=54-5\)

\(x\times2=49\)

\(x=\dfrac{49}{2}\)

24,5

Đáp án là C