Question

Tìm gt lớn nhất:   a) A= 2x-x²                                      b) B=19-6x-9x²

Tìm gt nhỏ nhất:  c) C=25x²+3y²-10x+11                           d) D=(x-3)²+(x-11)²

Answer 1

câu 1: Max

a) \(A=-\left(x^2-2x+1\right)+1=1-\left(x-1\right)^2\)

ta có: \(\left(x-1\right)^2\ge0\Leftrightarrow-\left(x-1\right)^2\le0\Leftrightarrow1-\left(x-1\right)^2\le1\Rightarrow MaxA=1\Leftrightarrow x=1\)

b) \(B=18-\left(9x^2+6x+1\right)=18-\left(3x+1\right)^2\le18\Rightarrow MaxB=18\Leftrightarrow x=-\frac{1}{3}\)

câu 2: Min

c) \(C=\left(25x^2-10x+1\right)+3y^2+10=\left(5x-1\right)^2+3y^2+10\)

ta có: \(\left(5x-1\right)^2\ge0;3y^2\ge0\Rightarrow\left(5x-1\right)^2+3y^2\ge0\Leftrightarrow\left(5x-1\right)^2+3y^2+10\ge10\Rightarrow MinC=10\Leftrightarrow x=\frac{1}{5};y=0\)