Question

[Nguyễn Xuân Nhi]

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