a: \(A=-x^2+2x-2\)
\(=-x^2+2x-1-1\)
\(=-\left(x-1\right)^2-1\le-1<0\forall x\)
=>A luôn âm với mọi x
b: \(B=-2x^2+8x-15\)
\(=-2x^2+8x-8-7\)
\(=-2\left(x^2-4x+4\right)-7=-2\left(x-2\right)^2-7\le-7<0\forall x\)
=>B luôn âm với mọi x
c: \(C=-\frac12x^4-2,5x^2-3\)
\(=-\frac12\left(x^4+5x^2+6\right)\)
\(=-\frac14\left\lbrack x^2\left(x^2+5\right)+6\right\rbrack\le-\frac14\cdot6=-\frac32<0\forall x\)
=>C luôn âm với mọi x
d: \(D=-2x^2-y^2+2xy-2x-2y-6\)
\(=-x^2+2xy-y^2+2x-2y-x^2-6\)
\(=-\left(x-y\right)^2+2\left(x-y\right)-1-x^2-5\)
\(=-\left\lbrack\left(x-y\right)^2-2\left(x-y\right)+1\right\rbrack-x^2-5=-\left(x-y-1\right)^2-x^2-5\le-5<0\forall x\)
=>D luôn âm với mọi x
