Ta có: \(a+b=c\Rightarrow\frac{a+b}{2}=\frac{c}{2}\Rightarrow\left(\frac{a+b}{2}\right)^2=\left(\frac{c}{2}\right)^2\)

Như vậy ta cần cm: \(ab\le\left(\frac{a+b}{2}\right)^2\Leftrightarrow4ab\le\left(a+b\right)^2\Leftrightarrow a^2+b^2\ge2ab\Leftrightarrow\left(a-b\right)^2\ge0\)(đúng)

Vậy ta có đpcm. 

\(a,8-2\sqrt{7}=\sqrt{7}^2-2\sqrt{7}+1^2=\left(\sqrt{7}-1\right)^2\)

\(b,8-2\sqrt{15}=\sqrt{5}^2-2.\sqrt{3}.\sqrt{5}+\sqrt{3}^2=\left(\sqrt{5}-\sqrt{3}\right)^2\)

\(c,8+4\sqrt{3}=2^2+2.2.\sqrt{3}+\sqrt{3}^2=\left(2+\sqrt{3}\right)^2\)

\(x^3-4x^2-12x+27=\left(x^3+27\right)-\left(4x^2+12x\right)\)\(=\left(x+3\right)\left(x^2-3x+9\right)-4x\left(x+3\right)\\ =\left(x+3\right)\left(x^2-3x+9-4x\right)=\left(x+3\right)\left(x^2-7x+9\right)\)

\(x^3-4x^2-12x+27\)

\(=x^3+3x^2-7x^2-21x+9x+27\)

\(=x^2\left(x+3\right)-7x\left(x+3\right)+9\left(x+3\right)\)

\(=\left(x+3\right)\left(x^2-7x+9\right)\)

ko biết đúng ko sai đưng ném đá

\(71+503,5\times2=x+\frac{140}{2}+1007\)

\(\Rightarrow71+503,5\times2=x+70+1007\)

\(\Rightarrow71+1007=x+70+1007\)

\(\Rightarrow1078=x+70+1007\)

\(\Rightarrow1078-1007=x+70\)

\(\Rightarrow71=x+70\)

\(\Rightarrow71-70=x\)

\(\Rightarrow x=1\)

\(71+503,5\cdot2=x+\frac{140}{2}+1007\)

\(\Leftrightarrow71+1007=x+70+1007\)

\(\Leftrightarrow1078=x+1077\)

\(\Leftrightarrow1078-x=1077\Leftrightarrow x=1\)

\(A=\left(6x-3y\right)+\left(4x^2-4xy+y^2\right)\) 

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

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

\(B=9x^2-\left(y^2-4y+4\right)\) 

   \(=9x^2-\left(y-2\right)^2\) 

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

A = ( 6x - 3y ) + (4x² - 4xy + y² )

A = 3.( 2x - y) + [ ( 2x )² - 2.2.x.y + y² ]

A = 3.( 2x - y ) + ( 2x - y )²

A = ( 2x - y ).(3 + 2x - y )

B = 9x² - ( y² - 4y + 4 )

B = ( 3x )² - ( y - 2 )²

B = ( 3x - y + 2 ).( 3x + y - 2 )

C = - 25x² + y² - 6y + 9

C =   ( y² - 2.3.y + 3² ) - ( 5x )²

C = ( y - 3 )² - ( 5x )²

C = (y - 3 - 5x ).( y - 3 +5x )

D = x² - 4x - y² -- 8y  - 12

D = ( x² - 4x + 4 ) - 4 - y² - 8y -12

D = ( x - 2.2x + 2² ) - ( y² + 2.4.y + 4² )

D = ( x - 2 )² - ( y + 4 )²

D = ( x - 2 + y + 4 ).( x - 2 - y - 4 )

D = ( x + y + 2 ).( x - y - 6 )

Ta có : 7^2017=7^2016×7=7^4.504×7=(....1)×7=(....7)

Vậy số tận cùng của 7^2017 là 7

Chúc bạn học tốt !!!

à khoan bn j ơi hai số chứ đâu pk 1 số đâu bn

( x + 3 )² + ( x - 3 ).( x + 3 )

= ( x + 3 ).( x + 3 + x - 3 )

= 2x.( x +3 )

Cách 1:\(\left(x+3\right)^2+\left(x-3\right)\left(x+3\right)\)

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

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

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

Cách 2: \(\left(x+3\right)^2+\left(x-3\right)\left(x+3\right)\)

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

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

E=(4x^2-4x+1)+(9y^2+6y+1)+(16z^2+8z+1)+1

E=(2x-1)^2+(3y-1)^2+(4z+1)^2+1

Vì (2x-1)^2>=0

      ........>=0

       .........>=0

nên E>= 1.dấu = xảy ra khi x=1/2

  y=1/3

z=1/4