d: Ta có: \(-x^2+2x-4y^2-4y+5\)
\(=-\left(x^2-2x+4y^2+4y-5\right)\)
\(=-\left(x^2-2x+1+4y^2+4y+1-7\right)\)
\(=-\left(x-1\right)^2-\left(2y+1\right)^2+7\le7\forall x,y\)
Dấu '=' xảy ra khi \(\left(x,y\right)=\left(1;-\dfrac{1}{2}\right)\)
e: Ta có: \(-8a^2+8a+3\)
\(=-8\left(a^2-a-\dfrac{3}{8}\right)\)
\(=-8\left(a^2-a+\dfrac{1}{4}-\dfrac{5}{8}\right)\)
\(=-8\left(a-\dfrac{1}{2}\right)^2+5\le5\forall a\)
Dấu '=' xảy ra khi \(a=\dfrac{1}{2}\)
f: Ta có: \(-\dfrac{9}{25}b^2+b\)
\(=-\left(\dfrac{9}{25}b^2-b\right)\)
\(=-\left(\dfrac{9}{25}b^2-2\cdot\dfrac{3}{5}b\cdot\dfrac{5}{6}+\dfrac{25}{36}-\dfrac{25}{36}\right)\)
\(=-\left(\dfrac{3}{5}b-\dfrac{5}{6}\right)^2+\dfrac{25}{36}\le\dfrac{25}{36}\forall b\)
Dấu '=' xảy ra khi \(b=\dfrac{25}{18}\)
a: Ta có: \(-x^2+4x+4\)
\(=-\left(x^2-4x-4\right)\)
\(=-\left(x^2-4x+4-8\right)\)
\(=-\left(x-2\right)^2+8\le8\forall x\)
b: Ta có: \(-16x^2-8x+4\)
\(=-\left(16x^2+8x-4\right)\)
\(=-\left(16x^2+8x+1-5\right)\)
\(=-\left(4x+1\right)^2+5\le5\forall x\)
Dấu '=' xảy ra khi \(x=-\dfrac{1}{4}\)
c: Ta có: \(-\left(3x+7\right)^2+2\left(3x+7\right)-17\)
\(=-\left(9x^2+42x+49\right)+6x+14-17\)
\(=-9x^2-42x-48+6x-3\)
\(=-9x^2-36x-51\)
\(=-\left(9x^2+36x+51\right)\)
\(=-\left(9x^2+2\cdot3x\cdot6+36+15\right)\)
\(=-\left(3x+6\right)^2-15\le-15\forall x\)
Dấu '=' xảy ra khi x=-2
