a)\(A=3\cdot\left|1-2x\right|-5\)
Vì \(\left|1-2x\right|\ge0\Rightarrow3\cdot\left|1-2x\right|\ge0\Rightarrow3\cdot\left|1-2x\right|-5\ge0-5=-5\)
\(\Rightarrow A\ge-5\)
\(\Rightarrow MIN_A=-5\Leftrightarrow\left|1-2x\right|=0\Leftrightarrow1-2x=0\Leftrightarrow2x=1\Leftrightarrow x=\frac{1}{2}\)
b)\(B=\left(2x^2+1\right)^4-3\)
Vì \(\left(2x^2+1\right)^4\ge1\Rightarrow\left(2x^2+1\right)^4-3\ge1-3=-2\)
\(\Rightarrow A\ge-2\)
\(\Rightarrow MIN_A=-2\Leftrightarrow\left(2x^2+1\right)^4=1\Leftrightarrow2x^2+1=1\Leftrightarrow2x^2=0\Leftrightarrow x=0\)
c)\(C=\left|x-\frac{1}{2}\right|+\left(y+2\right)^2+11\)
Vì \(\left|x-\frac{1}{2}\right|\ge0,\left(y+2\right)^2\ge0\Rightarrow\left|x-\frac{1}{2}\right|+\left(y+2\right)^2+11\ge0+0+11=11\)
\(\Rightarrow A\ge11\)
\(\Rightarrow MIN_A=11\Leftrightarrow\left|x-\frac{1}{2}\right|=0\Leftrightarrow x=\frac{1}{2},\left(y+2\right)^2=0\Leftrightarrow y+2=0\Leftrightarrow y=-2\)
bài nay lớp 9 thật ak
hiện tại mk lớp 7 và cô giáo giao cho mk bài này 