Question

tìm giá trị lớn nhất 

A= 5 - 8x - x² 

B = 5 - x² + 2x - 4y² -4y

Answer 1

A=-(x²+8x+16)+21<=21  (tự làm tiếp)

B=-(x²-2x+1)-(4y²+4y+1)+7

=-(x-1)²-(2y+1)²+7<=7

Answer 2

\(A=5-8x-x^2\)

\(A=-x^2-8x+5\)

\(-A=x^2+8x-5\)

\(-A=x^2+4x+4x+16-21\)

\(-A=x.\left(x+4\right)+4.\left(x+4\right)-21\)

\(-A=\left(x+4\right).\left(x+4\right)-21\)

\(A=-\left(x+4\right)^2-21\le-21\)

Dấu = xảy ra khi A = -21 \(\Leftrightarrow-\left(x+4\right)^2-21=-21\)

 \(\Leftrightarrow-\left(x+4\right)^2=0\Rightarrow x+4=0\Rightarrow x=-4\)