Giải:

1) \(9x^2-12xy+4y^2-3\)

\(=\left(9x^2-12xy+4y^2\right)-3\)

\(=\left(3x-2y\right)^2-3\)

2) \(x^2+4x+1\)

\(=x^2+4x+4-3\)

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

3) \(x^2-4x+7\)

\(=x^2-4x+4+3\)

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

4) \(x^2+6x+15\)

\(=x^2+6x+9+6\)

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

5) \(x^2-x+\dfrac{1}{3}\)

\(=x^2-x+\dfrac{1}{4}+\dfrac{1}{12}\)

\(=\left(x-\dfrac{1}{2}\right)^2+\dfrac{1}{12}\)

6) \(\dfrac{1}{4}x^2+x\)

\(=x\left(\dfrac{1}{4}x+1\right)\)

7) \(3x^2+2x+1\)

\(=x^2+2x+1+2x^2\)

\(=\left(x+1\right)^2+2x^2\)

8) \(2x^2-2x+1\)

\(=x^2-2x+1+x^2\)

\(=\left(x-1\right)^2+x^2\)

9) \(10a^2+5b^2+12ab+4a-6b+15\)

\(=a^2+b^2+9a^2+12ab+4b^2+4a-6b+15\)

\(=9a^2+12ab+4b^2+a^2+4a-6b+b^2+15\)

\(=\left(3a+2b\right)^2+a\left(a+4\right)-b\left(6-b\right)+15\)

Vậy ...

Giải;

1) \(9x^2-12xy+4y^2-3\)

\(=\left(9x^2-12xy+4y^2\right)-3\)

\(=\left(3x-2y\right)^2-3\)

2) \(x^2+4x+1\)

\(=x^2+4x+4-3\)

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

3) \(x^2-4x+7\)

\(=x^2-4x+4+3\)

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

4) \(x^2+6x+15\)

\(=x^2+6x+9+6\)

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

5) \(x^2-x+\dfrac{1}{3}\)

\(=x^2-x+\dfrac{1}{4}+\dfrac{1}{12}\)

\(=\left(x-\dfrac{1}{2}\right)^2+\dfrac{1}{12}\)

6) \(\dfrac{1}{4}x^2+x\)

\(=x\left(\dfrac{1}{4}x+1\right)\)

7) \(3x^2+2x+1\)

\(=x^2+2x+1+2x^2\)

\(=\left(x+1\right)^2+2x^2\)

8) \(2x^2-2x+1\)

\(=x^2-2x+1+x^2\)

\(=\left(x-1\right)^2+x^2\)

9) \(10a^2+5b^2+12ab+4a-6b+15\)

\(=a^2+b^2+9a^2+12ab+4b^2+4a-6b+15\)

\(=9a^2+12ab+4b^2+a^2+4a-6b+b^2+15\)

\(=\left(3a+2b\right)^2+a\left(a+4\right)-b\left(6-b\right)+15\)

Vậy ...

Giải:

1) \(9x^2-12xy+4y^2-3\)

\(=\left(3x-2y\right)^2-3\)

\(=\left(3x-2y-\sqrt{3}\right)\left(3x-2y+\sqrt{3}\right)\) (Bước này chắc không cần)

2) \(x^2+4x+1\)

\(=x^2+4x+4-3\)

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

\(=\left(x+2-\sqrt{3}\right)\left(x+2+\sqrt{3}\right)\)

(Bước này chắc không cần)

3) \(x^2-4x+7\)

\(=x^2-4x+4+3\)

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

4) \(x^2+6x+15\)

\(=x^2+6x+9+6\)

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

5) \(x^2-x+\dfrac{1}{3}\)

\(=x^2-x+\dfrac{1}{4}+\dfrac{1}{12}\)

\(=\left(x-\dfrac{1}{2}\right)^2+\dfrac{1}{12}\)

6) \(\dfrac{1}{4}x^2+x\)

\(=\left(\dfrac{1}{2}x\right)^2+x+1-1\)

\(=\left(\dfrac{1}{2}x+1\right)^2-1\)

7) \(3x^2+2x+1\)

\(=x^2+2x+1+2x^2\)

\(=\left(x+1\right)^2+2x^2\)

8) \(2x^2-2x+1\)

\(=x^2-2x+1+x^2\)

\(=\left(x-1\right)^2+x^2\)

9) \(10a^2+5b^2+12ab+4a-6b+15\)

\(=4a^2+6a^2+4b^2+b^2+12ab+4a-6b+15\)

\(=\left(6a^2+b^2+12ab\right)+4a+4a^2-6b+4b^2+15\)

\(=\left(6a+b\right)^2+4a\left(1+a\right)-2b\left(3+2b\right)+15\)

Giải:

1) \(9x^2-12xy+4y^2-3\)

\(=\left(9x^2-12xy+4y^2\right)-3\)

\(=\left(3x-2y\right)^2-3\)

2) \(x^2+4x+1\)

\(=x^2+4x+4-3\)

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

3) \(x^2-4x+7\)

\(=x^2-4x+4+3\)

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

4) \(x^2+6x+15\)

\(=x^2+6x+9+6\)

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

5) \(x^2-x+\dfrac{1}{3}\)

\(=x^2-x+\dfrac{1}{4}+\dfrac{1}{12}\)

\(=\left(x-\dfrac{1}{2}\right)^2+\dfrac{1}{12}\)

6) \(\dfrac{1}{4}x^2+x\)

\(=x\left(\dfrac{1}{4}x+1\right)\)

7) \(3x^2+2x+1\)

\(=x^2+2x+1+2x^2\)

\(=\left(x+1\right)^2+2x^2\)

8) \(2x^2-2x+1\)

\(=x^2-2x+1+x^2\)

\(=\left(x-1\right)^2+x^2\)

9) \(10a^2+5b^2+12ab+4a-6b+15\)

\(=a^2+b^2+9a^2+12ab+4b^2+4a-6b+15\)

\(=9a^2+12ab+4b^2+a^2+4a-6b+b^2+15\)

\(=\left(3a+2b\right)^2+a\left(a+4\right)-b\left(6-b\right)+15\)

Vậy ...

1. \(x^6-2x^3+1=0\Leftrightarrow\left(x^3-1\right)^2=0\Leftrightarrow x=1\)

2. \(x^6+\dfrac{1}{4}x^3+\dfrac{1}{64}=0\Leftrightarrow\left(x^3\right)^2+2.x^3.\dfrac{1}{8}+\left(\dfrac{1}{8}\right)^2=0\Leftrightarrow\left(x+\dfrac{1}{8}\right)^2=0\Leftrightarrow x=-\dfrac{1}{2}\)4. \(x^3-10x^2+25x=0\Leftrightarrow x^3-5x^2-5x^2+25x=0\)

\(\Leftrightarrow x^2\left(x-5\right)-5x\left(x-5\right)=0\)

\(\Leftrightarrow x\left(x-5\right)^2=0\Leftrightarrow x=5\)

5. \(\dfrac{1}{4}x^3-3x^2+9x=0\)

\(\Leftrightarrow x\left(\dfrac{1}{4}x^2-3x+9\right)=0\)

\(\Leftrightarrow x\left[\left(\dfrac{1}{2}x\right)^2-2.\dfrac{1}{2}x.3+3^2\right]=0\)

\(\Leftrightarrow x\left(\dfrac{1}{2}x-3\right)^2=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x=6\end{matrix}\right.\)

6. \(x^5-16x=0\Leftrightarrow x\left(x^4-16\right)=0\Leftrightarrow x\left(x^2-4\right)\left(x^2+4\right)=0\)

\(\Leftrightarrow x\left(x-2\right)\left(x+2\right)\left(x^2+4\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x=2\\x=-2\\x^2=-4\left(l\right)\end{matrix}\right.\)

7. \(4x^2+4x-3=0\Leftrightarrow4x^2-2x^2-6x-3=0\)

\(\Leftrightarrow2x\left(2x-1\right)-3\left(2x-1\right)=0\)

\(\Leftrightarrow\left(2x-1\right)\left(2x+3\right)=0\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{1}{2}\\x=-\dfrac{3}{2}\end{matrix}\right.\)

8. \(4x^2+28x+48=0\Leftrightarrow4x^2+12x+14x+48=0\)

\(\Leftrightarrow4x\left(x+3\right)+12\left(x+4\right)=0\)

\(\Leftrightarrow\left(4x+12\right)\left(x+3\right)=0\Leftrightarrow\left[{}\begin{matrix}x=-3\\x=-4\end{matrix}\right.\)

9. \(9x^2-12x+3=0\Leftrightarrow9x^2-9x-3x+3=0\Leftrightarrow9x\left(x-1\right)-3\left(x-1\right)=0\Leftrightarrow\left(x-1\right)\left(9x-3\right)=0\Leftrightarrow\left[{}\begin{matrix}x=1\\x=\dfrac{1}{3}\end{matrix}\right.\)

|2 - x|² + 6x - 3 = 0

<=> (x - 2)² + 6x - 3 = 0

<=> x² - 4x + 4 + 6x - 3 = 0

<=> x² + 2x + 1 = 0

<=> (x + 1)² = 0

<=> x + 1 = 0

<=> x = -1

Bắt phải thể hiện -_-

bn kiểm tra giúp mk đề 2 câu cuối , mk làm ko ra

Khó quá,hay quá !!!

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