\(A=\left(2+1\right)\left(2^2+1\right)...\left(2^{64}+1\right)\)

\(A=1\cdot\left(2+1\right)\left(2^2+1\right)...\left(2^{64}+1\right)\)

\(A=\left(2-1\right)\left(2+1\right)\left(2^2+1\right)...\left(2^{64}+1\right)\)

\(A=\left(2^2-1\right)\left(2^2+1\right)...\left(2^{64}+1\right)\)

\(A=\left(2^4-1\right)\left(2^4+1\right)...\left(2^{64}+1\right)\)

\(A=\left(2^{64}-1\right)\left(2^{64}+1\right)\)

\(A=2^{128}-1\)

ttpq_Trần Thanh Phương  đúng đó !!!

Xin lỗi  mới học lớp 7!***~~~@

Đặt  x = \(\frac{1}{2a+1},y=\frac{1}{2b+1},z=\frac{1}{2c+1}\)

Khi đó \(a=\frac{1-x}{2x},b=\frac{1-y}{2y},c=\frac{1-z}{2z}\)

Ta thấy 0 < x, y, z < 1 và x + y + z \(\ge1\)

Bất đẳng thức cần chứng minh trở thành :

\(\frac{x}{3-2x}+\frac{y}{3-2y}+\frac{z}{3-2z}\ge\frac{3}{7}\)

Áp dụng bất đẳng thức Bunhiacốpxki ta có :

\(\frac{x}{3-2x}+\frac{y}{3-2y}+\frac{z}{3-2z}\)

\(=\frac{x^2}{3x-2x^2}+\frac{y^2}{3y-2y^2}+\frac{z^2}{3z-2z^2}\)

\(\ge\frac{\left(x+y+z\right)^2}{3\left(x+y+z\right)-2\left(x^2+y^2+z^2\right)}\)

\(\ge\frac{\left(x+y+z\right)^2}{3\left(x+y+z\right)-\frac{2}{3}\left(x+y+z\right)^2}\)

\(=\frac{3}{\frac{9}{x+y+z}-2}\ge\frac{3}{7}\)

Cbht

\(3x^3-19x^2+44x-32=3x^3-4x^2-15x^2+20x+24x-32\)

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

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