Question

Tìm GTNN

a) A=x(x-3)(x-4)(x-7)

b)B=2x²+y²-2xy-2x+3

c)C=x²+xy+y²-3x-3y

d)D=(x+8)⁴+(x+6)⁴

e)E=x⁴-6x³+10x²-6x+9

Answer 1

TL:

\(B=2x^2+y^2-2xy-2x+3\)

    \(=\left(x^2-2xy+y^2\right)+(x^2-2x+1)+2\)

    \(=\left(x-y\right)^2+\left(x-1\right)^2+2\ge2\forall x;y\)

Answer 2

\(D=\left(x+8\right)^4+\left(x+6\right)^4\ge0\forall x\)

Dấu"=" xảy ra<=> \(\hept{\begin{cases}\left(x+8\right)^4=0\\\left(x+6\right)^4=0\end{cases}}\)

\(\Rightarrow\hept{\begin{cases}x=-8\\x=-6\end{cases}}\)