Bài 1 :Rút gọn

\(\left(4x^2-3y\right)a2y-\left(3x^2-4y\right)3y\)

\(4x^2\left(5x-3y\right)-x^2\left(4x+y\right)\)

\(2ax^2-a\left(1+2x^2\right)-\left\{a-x\left(x+a\right)\right\}\)

Bài 2:Tìm x

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

b)\(4x\left(3x+2\right)-6x\left(2x+5\right)+21\left(x-1\right)=0\)

Bài 3:Rút gọn

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

giải pt , \(\sqrt{x^4+4x^2}+\sqrt{x+x^2}=\sqrt{\left(x^2+\sqrt{x}\right)^2+9x^2}.\)

\(x=0\)

\(x^3=0\)

\(x^3=2.0.\sqrt{0}\)

\(x^3=2x\sqrt{x}\)

\(x^3=2x\sqrt{x}\)     

\(4\left(x^3-2x\sqrt{x}\right)^2=0\)

\(4\left(x^6-4x^4\sqrt{x}+4x^2x\right)=0\)

\(4x^6-16x^4\sqrt{x}+16x^2x=0\)

\(4x^6+16x^3=16x^4\sqrt{x}\)

\(16x^4+4x^5+4x^6+16x^3=16x^4+4x^5+16x^4\sqrt{x}\)

\(4x^3\left(x+1\right)\left(x^2+4\right)=4\left(4x^4+4x^4\sqrt{x}+x^4.x\right)\)

\(4x^3\left(x+1\right)\left(x^2+4\right)=4\left(2x^2+x^2\sqrt{x}\right)^2\)

\(2\sqrt{2x^3\left(x+1\right)\left(x^2+4\right)}=2\left(2x^2+x^2\sqrt{x}\right)\)

\(x^4+x^2+4x^2+x+2\sqrt{2x^3\left(x+1\right)\left(x^2+4\right)}=2\left(2x^2+x^2\sqrt{x}\right)+x^4+x^2+4x^2+x\)

\(\left(\sqrt{x^4+4x^2}+\sqrt{x^2+x}\right)^2=\left(x^4+2x^2\sqrt{x}+x\right)+9x^2\)

\(\sqrt{x^4+4x^2}+\sqrt{x^2+x}=\sqrt{\left(x^2+\sqrt{x}\right)^2+9x^2}\)

vậy x=0 là nghiệm của pt  =)) 

Tìm x biết : (đề không sai)

1.\(-4x\left(x-7\right)+4x\left(x^2-5\right)\) \(=28x^2-13\)

2.\(\left(4x^2-5x\right)\left(3x+2\right)-7x\left(x-7\right)\)= \(\left(-4+x\right)\left(-2x+3\right)+12x^3+2x^2\)

3.\(\left(-4x^2-3\right)\left(2x+5\right)-\left(8x-3\right)\) \(\left(-x^2+2\right)=-5x^2\left(x-6\right)-3x^2-4\)

4.\(\left(x-7\right)\left(x+5\right)-\left(x-3\right)\left(x-2\right)\) \(=15x^2\left(x+1\right)-\left(3x^2-1\right)\) \(\left(5x^2-2\right)-21x^2\)

5.\(\left(x-3\right)\left(-x+10\right)+\left(x-8\right)\left(x+3\right)\) \(=\left(5x^2-1\right)\left(x+3\right)-5x^3-15x^2\)

6.\(\left(-2x^2+5\right)\left(-x+3\right)-x^2\left(2x-6\right)\) \(=\left(x-1\right)\left(x+1\right)-\left(x-2\right)\left(x+4\right)\)

Câu 1: Rút gọn các biểu thức sau:

1. \(\left(x+y-z\right)^2+\left(y-z\right)^2+2z\left(z-y\right)\)

2. \(\left(3x+4\right)^2+\left(x-4\right)^2+2\left(3x+4\right)\left(x-4\right)\)

3.\(\left(3+1\right)\left(3^2+1\right)\left(3^4+1\right)\left(3^8+1\right)\left(3^{16}+1\right)\left(3^{32}+1\right)\)

4. \(2x\left(2x-1\right)^2-3x\left(x+3\right)\left(x-3\right)-4x\left(x+1\right)\)

5. \(\left(3+1\right)\left(3^2+1\right)\left(3^4+1\right)\left(3^8+1\right)\left(3^{16}+1\right)\left(3^{32}+1\right)\)

Câu 2: Tìm x

1. \(4\left(x+1\right)^2+\left(2x-1\right)^2-8\left(x-1\right)\left(x+1\right)=1\)

2. \(\left(3x+1\right)^2+\left(5x-2\right)^2=34\left(x+2\right)\left(x-2\right)\)

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

4. \(4x^2-9-x\left(2x-3\right)=0\)

5. \(4x^2-12x+9=0\)

Câu 3: Tìm GTNN

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

Câu 4: Cho \(a^2+b^2+c^2=ab+bc+ac\) . Chứng minh rằng a=b=c

Giải phương trình:

1, \(\left(x^2+x+1\right)\left(x^4+2x^3+7x^2+26x+37\right)=5\left(x+3\right)^3\)

2, \(\left(x+1\right)^3+\left(x+3\right)^3+6\left(x+1\right)\left(x+7\right)\left(x+3\right)=8\left(x+2\right)^3\)

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

4, \(\dfrac{\left(x+1\right)^3}{3x+1}+\dfrac{x^3+5x+2}{x^3+2x+1}=x+3\)

5, \(\dfrac{5x^3+x^2+x+1}{4x^2+1}+\dfrac{6\left(4x^2+1\right)}{x^3+x^2+1}=x+7\)

6, \(\left(x^2-4x+1\right)^3+\left(8x-x^2+4\right)^3+\left(x-5\right)^3=125x^3\)

giải pt

a) \(x^2+4x-3\left|x+2\right|+4=0\)

b) \(\left(x+2\right)^2-3\left|x+2\right|-4=0\)

c) \(\left(x^2-3\right)^2-6\left|x^2-3\right|+5=0\)

d) \(\frac{x^2-4x+4}{x^2-2x+1}+\frac{\left|2x-4\right|}{x-1}=3\)

e) \(\left|\frac{2x-1}{x+2}\right|-2\left|\frac{x+2}{2x-1}\right|=1\)

f) \(x^2+\frac{1}{x^2}-10=2\left|x-\frac{1}{x}\right|\)