3) 5x2 + y2 -4xy - 2y + 8x + 2013
= ( 4x2 + y2 -4xy -2y + 8x ) + x2 + 2013
= ( 2x - y +1)2 + x2 +2013
Vì ( 2x-y+1)2 \(\ge\)0 \(\forall x,y\); x2 \(\ge\)0\(\forall x\)
=> (2x - y+1)2 + x2 \(\ge\)0
=> ( 2x-y +1)2 +x2 + 2013\(\ge\)0
hay A \(\ge0\)\(\forall x,y\)=> A ko âm
Giúp mk phần 1 và phần 2 vs!!!
HELP ME PLEASE!!!
1\(\left(15x-1\right)^2+3\left(7x+3\right)\left(x+1\right)-\left(x^2-73\right)\))
\(=\left(15x-1\right)^2+21x^2+30x+9-x^2+73\)
\(=\left(15x-1\right)^2+20x^2+30x+82\)
\(=\left(15-1\right)^2+20\left(x^2+\frac{3}{2}x+\frac{9}{16}\right)+\frac{283}{4}\)
\(=\left(15x-1\right)^2+20\left(x+\frac{3}{4}\right)^2+\frac{283}{4}\)
Vì \(\left(15x-1\right)^2;20\left(x+\frac{3}{4}\right)^2;\frac{283}{4}\ge0\forall x\)=> Biểu thức ko âm
= nhat anh dep trai nghin gai theo