TL :

a) 6¹⁷ = 2¹⁷ . 3¹⁷

    2³⁴ = 2¹⁷ . 2¹⁷

Có : 3 > 2

=> 3¹⁷ > 2¹⁷

=> 2¹⁷ . 3¹⁷ > 2¹⁷ . 2¹⁷

=> 6¹⁷ > 2³⁴

Hok tốt

Bài làm

\(\frac{2^{10}.3^{31}+2^{40}.3^6}{2^{11}.3^{11}+2^{41}.3^6}\)

\(=\frac{2^{10}.\left(3^{11}+2^{30}.3^6\right)}{2^{11}.\left(3^{11}+2^{30}.3^6\right)}\)

\(=\frac{1}{2}\)

~ K chắc ~

# Học tốt #

\(\frac{2^{10}.3^{31}+2^{40}.3^6}{2^{11}.3^{31}+2^{41}.3^6}=\frac{2^{10}.3^6\left(3^{25}+2^{30}\right)}{2^{11}.3^6\left(3^{25}+2^{30}\right)}=\frac{1}{2}\)

Ta có : \(x^2+2x+2=x^2+x+x+1+1=\left[x^2+x\right]+\left[x+1\right]+1\)

\(=x\left[x+1\right]+\left[x+1\right]+1\)

\(=\left[x+1\right]^2+1\ge1>0\forall x\)

Vậy đa thức trên ko có nghiệm

Ta có: x² + 2x + 2 = (x² + 2x + 1) + 1 = (x + 1)² + 1 \(\ge\)1 với mọi x

=> x² + 2x + 2 ko có nghiệm nguyên

Ta có: \(\hept{\begin{cases}\left|x+1\right|\ge0\\\left|x+3\right|\ge0\\\left|x+5\right|\ge0\end{cases}}\Rightarrow VT\ge0\)

\(\Leftrightarrow3x-4\ge\Leftrightarrow x\ge\frac{4}{3}\)

\(\Rightarrow pt\Leftrightarrow3x+9=3x-4\Leftrightarrow9=-4\)(vô lí)

Vậy pt vô nghiệm

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

*Nếu \(x\le3\)thì \(\left(1\right)\Leftrightarrow\left|2x-3\right|+3-x=4x-1\)

\(\Leftrightarrow\left|2x-3\right|=5x-4\)(2)

+) TH1: \(x\ge\frac{3}{2}\)thì \(\left(2\right)\Leftrightarrow2x-3=5x-4\)

\(\Leftrightarrow-3x=-1\Leftrightarrow x=\frac{1}{3}\left(L\right)\)

+) TH2: \(x< \frac{3}{2}\)thì \(\left(2\right)\Leftrightarrow3-2x=5x-4\)

\(\Leftrightarrow-7x=-7\Leftrightarrow x=1\left(TM\right)\)

*Nếu \(x>3\)thì \(\left(1\right)\Leftrightarrow\left|2x-3\right|-3+x=4x-1\)

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

+) TH1: \(x\ge\frac{3}{2}\)thì \(\left(3\right)\Leftrightarrow2x-3=3x+2\Leftrightarrow-x=5\Leftrightarrow x=-5\left(L\right)\)

+) TH2: \(x< \frac{3}{2}\)thì \(\left(3\right)\Leftrightarrow3-2x=3x+2\Leftrightarrow-5x=-1\Leftrightarrow x=\frac{1}{5}\left(L\right)\)

Vậy x = 1