A=10

B=5

C=2

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

b) \(\left(3x-\frac{1}{8}y\right)^2=9x^2-\frac{3}{4}xy+\frac{1}{64}y^2\)

c) \(\left(-6x-\frac{2}{5}\right)^2=36x^2+\frac{24}{5}x+\frac{4}{25}\)

d) \(\left(xy^2+1\right)\left(xy^2-1\right)=x^2y^4-1\)

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

f) \(\left(\frac{1}{2}x-\frac{1}{3}y-1\right)^2=\frac{1}{4}x^2+\frac{1}{9}y^2+1-\frac{1}{3}xy-x+\frac{2}{3}y\)

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

b, \(\left(3x-\frac{1}{8}y\right)^2=9x^2-\frac{3}{4}xy+\frac{1}{64}y^2\)

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

Bài làm:

Ta có: \(3\left(3-2x^2\right)+3x\left(2x-1\right)=9\)

\(\Leftrightarrow9-6x^2+6x^2-3x=9\)

\(\Leftrightarrow3x=0\)

\(\Rightarrow x=0\)

\(3\left(2-2x^2\right)+3x\left(2x-1\right)=9\)

\(\Leftrightarrow3\left(2-2x^2+2x^2-x\right)=9\)

\(\Leftrightarrow2-x=3\)

\(\Leftrightarrow x=-1\)

\(A=5-8x+x^2=-8x+x^2+6-11\)

\(=\left(x-4\right)^2-11\)

Vì \(\left(x-4\right)^2\ge0\forall x\)\(\Rightarrow\left(x-4\right)^2-11\ge-11\)

Dấu "=" xảy ra \(\Leftrightarrow\left(x-4\right)^2=0\Leftrightarrow x-4=0\Leftrightarrow x=4\)

Vậy Amin = - 11 <=> x = 4

\(B=\left(2-x\right)\left(x+4\right)=-x^2-2x+8\)

\(=-\left(x^2+2x+1\right)+9=-\left(x+1\right)^2+9\)

Vì \(\left(x+1\right)^2\ge0\forall x\)\(\Rightarrow-\left(x+1\right)^2+9\le9\)

Dấu "=" xảy ra \(\Leftrightarrow-\left(x+1\right)^2=0\Leftrightarrow x+1=0\Leftrightarrow x=-1\)

Vậy Bmax = 9 <=> x = - 1

a) \(A=x\left(x+2\right)+y\left(y-2\right)-2xy+37\)

\(=x^2+2x+y^2-2y-2xy+37\)

\(=\left(x^2-2xy+y^2\right)+\left(2x-2y\right)+37\)

\(=\left(x-y\right)^2+2\left(x-y\right)+37\)

Thay \(x-y=7\)vào biểu thức ta được: 

\(A=7^2+2.7+37=49+14+37=100\)

b) Ta có: \(x+y=3\)\(\Rightarrow\left(x+y\right)^2=9\)\(\Rightarrow x^2+y^2+2xy=9\)

mà \(x^2+y^2=5\)\(\Rightarrow5+2xy=9\)

\(\Rightarrow2xy=4\)\(\Rightarrow xy=2\)

Vậy \(xy=2\)

a) A = x( x + 2 ) + y( y - 2 ) - 2xy + 37

= x² + 2x + y² - 2y - 2xy + 37

= ( x² - 2xy + y² ) + ( 2x - 2y ) + 37

= ( x - y )² + 2( x - y ) + 37

Thế x - y = 7 vào A ta được :

A = 7² + 2.7 + 37 = 49 + 14 + 37 = 100

Vậy A = 100 khi x - y = 7

b) x + y = 3 => ( x + y )² = 9

=> x² + 2xy + y² = 9

=> 5 + 2xy = 9 ( sử dụng gt x² + y² = 5 )

=> 2xy = 4

=> xy = 2 

\(2\left(a^2+b^2\right)=\left(a+b\right)^2\)

\(\Leftrightarrow2\left(a^2+b^2\right)-\left(a+b\right)^2=0\)

\(\Leftrightarrow\left(2a^2+2b^2\right)-\left(a^2+2ab+b^2\right)=0\)

\(\Leftrightarrow2a^2+2b^2-a^2-2ab-b^2=0\)

\(\Leftrightarrow a^2-2ab+b^2=0\)

\(\Leftrightarrow\left(a-b\right)^2=0\)

\(\Leftrightarrow a-b=0\)

\(\Leftrightarrow a=b\)( đpcm )

2( a² + b² ) = ( a + b )²

<=> 2a² + 2b² = a² + 2ab + b²

<=> 2a² + 2b² - a² - 2ab - b² = 0

<=> a² - 2ab + b² = 0

<=> ( a - b )² = 0 (*)

( a - b )² ≥ 0 ∀ a, b

Đẳng thức xảy ra ( tức (*) ) <=> a - b = 0 => a = b ( đpcm )

x⁶-1 =0

x^(6-1)=0

x⁵    =0

      x=0

Đúng chưa?

x⁶ - 1 = 0

<=> x⁶ = 1

<=> x⁶ = ( ±1 )⁶

<=> x = ±1

To ko thay gi