a: \(\left|x-2\right|>=0\forall x\)
=>\(3\left|x-2\right|>=0\forall x\)
=>\(3\left|x-2\right|+5>=5\forall x\)
Dấu = xảy ra khi x-2=0
=>x=2
b: \(2\left|x-\dfrac{1}{5}\right|>=0\forall x\)
\(\left|2-3y\right|>=0\forall y\)
Do đó: \(2\left|x-\dfrac{1}{5}\right|+\left|2-3y\right|>=0\forall x,y\)
=>\(2\left|x-\dfrac{1}{5}\right|+\left|2-3y\right|+2>=2\forall x,y\)
Dấu = xảy ra khi \(\left\{{}\begin{matrix}x-\dfrac{1}{5}=0\\2-3y=0\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}x=\dfrac{1}{5}\\y=\dfrac{2}{3}\end{matrix}\right.\)
c: \(\left|2x-5\right|>=0\) với mọi x
=>\(\left|2x-5\right|+1>=1\forall x\)
=>\(\dfrac{7}{\left|2x-5\right|+1}< =\dfrac{7}{1}=7\forall x\)
=>\(-\dfrac{7}{\left|2x-5\right|+1}>=-7\forall x\)
Dấu = xảy ra khi 2x-5=0
=>x=5/2
d: \(\left|4x+1\right|>=0\) với mọi x
=>\(-\left|4x+1\right|< =0\forall x\)
=>\(-\left|4x+1\right|+2< =2\forall x\)
=>\(\dfrac{3}{2-\left|4x+1\right|}>=\dfrac{3}{2}\forall x\)
Dấu '=' xảy ra khi 4x+1=0
=>x=-1/4
e: \(\left(3x-2\right)^2>=0\forall x\)
=>\(\left(3x-2\right)^2+0,5>=0,5\forall x\)
Dấu '=' xảy ra khi 3x-2=0
=>x=2/3
f: \(\left(x-\dfrac{1}{2}\right)^2>=0\forall x\)
\(\left(2y-3\right)^2>=0\forall y\)
Do đó: \(\left(x-\dfrac{1}{2}\right)^2+\left(2y-3\right)^2>=0\forall x,y\)
=>\(\left(x-\dfrac{1}{2}\right)^2+\left(2y-3\right)^2-\dfrac{1}{5}>=-\dfrac{1}{5}\forall x,y\)
Dấu '=' xảy ra khi x-1/2=0 và 2y-3=0
=>x=1/2 và y=3/2
