a)\(A=3.\left|1-2x\right|-5\)
+Có: \(\left|1-2x\right|\ge0với\forall x\\ \Rightarrow3.\left|1-2x\right|-5\ge-5\\ \Leftrightarrow A\ge-5\)
+Dấu ''='' xảy ra khi \(\left|1-2x\right|=0\Leftrightarrow x=\frac{1}{2}\)
+Vậy \(A_{min}=-5\) khi \(x=\frac{1}{2}\)
b)\(B=\left(2x^2+1\right)^4-3\)
+Có:\(\left(2x^2+1\right)^4\ge0với\forall x\\ \Rightarrow\left(2x^2+1\right)^4-3\ge-3\\ \Leftrightarrow B\ge-3\)
+Dấu "=" xảy ra khi \(\left(2x^2+1\right)^4=0\Leftrightarrow x\in\varnothing\)
+Vậy \(B_{min}=-3\) khi \(x\in\varnothing\)
c)\(\left|x-\frac{1}{2}\right|+\left(y+2\right)^2+11\)
+Có:\(\left|x-\frac{1}{2}\right|\ge0với\forall x\\ \left(y+2\right)^2\ge0với\forall x\\ \Rightarrow\left|x-\frac{1}{2}\right|+\left(y+2\right)^2+11\ge11\\ \Leftrightarrow C\ge11\)
+Dấu "=" xảy ra khi
\(\left|x-\frac{1}{2}\right|=0\Leftrightarrow x=\frac{1}{2}\)
\(\left(y+2\right)^2=0\Leftrightarrow y=-2\)
+Vậy \(C_{min}=11\) khi \(x=\frac{1}{2},y=-2\)
