a: \(x^4+y^4+z^2\ge2x\left(xy^2-x+z+1\right)\)
=>\(x^4+y^4+z^2\ge2x^2y^2-2x^2+2xz+2x\)
=>\(x^4-2x^2y^2+y^4+\left(z^2-2xz+x^2\right)+\left(x^2-2x+1\right)\ge0\)
=>\(\left(x^2-y^2\right)^2+\left(z-x\right)^2+\left(x-1\right)^2\ge0\) (luôn đúng)
b: \(a^2+5b^2-4ab+2a-6b+3>0\)
\(\Rightarrow a^2-4ab+4b^2+2a-6b+b^2+3>0\)
=>\(\left(a-2b\right)^2+2a-4b+b^2-2b+3>0\)
=>\(\left(a-2b\right)^2+2\left(a-2b\right)+1+b^2-2b+1+1>0\)
=>\(\left(a-2b+1\right)^2+\left(b-1\right)^2+1>0\) (luôn đúng)
c: \(a^2+2b^2-2ab+2a-4b+2\ge0\)
=>\(a^2-2ab+b^2+2a-2b+b^2-2b+2\ge0\)
=>\(\left(a-b\right)^2+2\left(a-b\right)+1+b^2-2b+1\ge0\)
=>\(\left(a-b+1\right)^2+\left(b-1\right)^2\ge0\) (luôn đúng)
