D = x² + 4xy + 4y² - z² + 2xt - t² 

 = (x + 2y)² - (z - t)² 

= (x + 2y - z + t)(x + 2y + z - t) 

Thay x = 10 ; y = 40 ; z = 30 ; t = 20 vào D 

\(\Rightarrow D=\left(10+40.2-30+20\right)\left(10+40.2+30-20\right)=80.100=8000\)

D = x\(^2\) + 4xy + 4y \(^2\) - z \(^2\) + 2zt - t \(^2\)

D = (x + 2y)\(^2\) - z\(^2\)+ z\(^2\) + 2zt + t\(^2\) - t\(^2\) 

D = (10 + 80)\(^2\) - 30\(^2\) + (z + t)\(^2\) - 20\(^2\) 

D = 90\(^2\) - 900 - 900 + (30 + 20)\(^2\) - 400

D = 8100 - 900 + 2500 - 400 

D =8600

HT

\(A=x\left(x+2\right)\left(x+4\right)\left(x+6\right)+8\)

\(=\left(x^2+6x\right)\left(x^2+6x+8\right)+8\)

\(=\left(x^2+6x+4\right)^2-4^2+8\)

\(=\left(x^2+6x+4\right)^2-8\ge-8\)

Dấu \(=\)khi \(x^2+6x+4=0\Leftrightarrow x=-3\pm\sqrt{5}\).

\(B=5+\left(1-x\right)\left(x+2\right)\left(x+3\right)\left(x+6\right)\)

\(=5-\left[\left(x-1\right)\left(x+6\right)\right].\left[\left(x+2\right)\left(x+3\right)\right]\)

\(=5-\left(x^2+5x-6\right)\left(x^2+5x+6\right)\)

\(=5-\left(x^2+5x\right)^2+6^2\)

\(=41-\left(x^2+5x\right)^2\le41\)

Dấu \(=\)khi \(x^2+5x=0\Leftrightarrow\orbr{\begin{cases}x=0\\x=-5\end{cases}}\)

\(C=\left(x+3\right)^4+\left(x-7\right)^4=\left[\left(x-2\right)+5\right]^4+\left[\left(x-2\right)-5\right]^4\)

\(=2\left(x-2\right)^4+300\left(x-2\right)^2+1250\ge1250\)

Dấu \(=\)khi \(x-2=0\Leftrightarrow x=2\).

B= 7800 nha

x=3

a=2

D = x\(^2\) + 2xy + y\(^2\) - z\(^2\) - 2zt - t\(^2\)

D = (x + y)\(^2\)  - z\(^2\) + z\(^2\) - 2zt + t\(^2\) - t\(^2\)

D = (89 + 11)\(^2\) +(z - t)\(^2\) - z\(^2\) - t\(^2\)

D = 100\(^2\) + (60 - 30)\(^2\) - 60\(^2\) - 30\(^2\)

D = 10 000 + 900 - 3600 - 900

D = 6400

Học tốt

D= 6400 nha

Ta có : A = 2 x ( X + 1 )  + X + 1 

= ( X + 1 ) x ( 2 + 1 )

= ( X + 1 ) x 3

Thay X = 99 vào biểu thức ta có :

( 99 + 1 ) x 3 = 300

e, A = 2x ( x + 1 ) + x + 1 tại x =99

    A = 2 x 99 x ( 99 + 1 ) + 99 + 1

    A =  198 x 100 + 100

    A =  19800 + 100

    A =  19900

Bài 5 : 

f, bạn xem lại đề hay là tìm x chứa tham số a ? 

g, \(x^2+3x-\left(2x+6\right)=0\Leftrightarrow x\left(x+3\right)-2\left(x+3\right)=0\)

\(\Leftrightarrow\left(x-2\right)\left(x+3\right)=0\Leftrightarrow x=-3;x=2\)

h, \(5x+20-x^2-4x=0\Leftrightarrow5\left(x+4\right)-x\left(x+4\right)=0\)

\(\Leftrightarrow\left(5-x\right)\left(x+4\right)=0\Leftrightarrow x=-4;x=5\)

m, \(x^3-5x^2-x+5=0\Leftrightarrow x^2\left(x-5\right)-\left(x-5\right)=0\)

\(\Leftrightarrow\left(x-1\right)\left(x+1\right)\left(x-5\right)=0\Leftrightarrow x=\pm1;x=5\)

n, \(x\left(x-3\right)-7x+21=0\Leftrightarrow x\left(x-3\right)-7\left(x-3\right)=0\)

\(\Leftrightarrow\left(x-7\right)\left(x-3\right)=0\Leftrightarrow x=3;x=7\)

x=7 nha

Bài 5 : 

a, \(2x\left(x-3\right)+x-3=0\Leftrightarrow\left(2x+1\right)\left(x-3\right)=0\Leftrightarrow x=-\frac{1}{2};x=3\)

b, \(x\left(x+1\right)-x-1=0\Leftrightarrow\left(x-1\right)\left(x+1\right)=0\Leftrightarrow x=\pm1\)

c, sửa đề  \(x^3-3x^2+x-3=0\Leftrightarrow x^2\left(x-3\right)+x-3=0\)

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

d, \(3x^2\left(2x-1\right)+1-4x^2=0\Leftrightarrow3x^2\left(2x-1\right)+\left(1-2x\right)\left(1+2x\right)=0\)

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

e, \(x^3+2x-x^2-2=0\Leftrightarrow x\left(x^2+2\right)-\left(x^2+2\right)=0\)

\(\Leftrightarrow\left(x-1\right)\left(x^2+2>0\right)=0\Leftrightarrow x=1\)

x=1 nha

a, \(\left(x+3\right)^2-\left(x+2\right)\left(x-2\right)=11\)

\(\Leftrightarrow x^2+6x+9-x^2+4=11\Leftrightarrow6x+2=0\Leftrightarrow x=-\frac{1}{3}\)

b, \(x^2-6x-7=0\Leftrightarrow\left(x+1\right)\left(x-7\right)=0\Leftrightarrow x=-1;x=7\)

c, \(\left(2x+1\right)^2-\left(3x-2\right)^2=0\Leftrightarrow\left(-x+3\right)\left(5x-1\right)=0\Leftrightarrow x=\frac{1}{5};x=3\)

x=3 nha

Bài 3 : 

\(D=40^2-28^2+32^2+80.32=40^2+2.40.32+32^2-28^2\)

\(=\left(40+32\right)^2-28^2=72^2-28^2=\left(72+28\right)\left(72-28\right)=46.100=4600\)

4600 nha