Question

aBài 1 : Tìm GTLN

a)A=-x²+ 4x

b)B=-2y²- 4y

c)C=-y²-x²-2x-y+3

d)D=-x²-y² + 2xy-6x+10

e)E=-3x²-3y²-6xy+5

Answer 1

a: \(A=-\left(x^2-4x\right)=-\left(x^2-4x+4-4\right)\)

\(=-\left(x-2\right)^2+4\le4\)

Dấu '=' xảy ra khi x=2

b: \(B=-2\left(y^2+2y+1-1\right)\)

\(=-2\left(y+1\right)^2+2\le2\)

Dấu '=' xảy ra khi y=-1

c: \(C=-\left(x^2+y^2+2x+y-3\right)\)

\(=-\left(x^2+2x+1+y^2+y+\dfrac{1}{4}-\dfrac{17}{4}\right)\)

\(=-\left(x+1\right)^2-\left(y+\dfrac{1}{2}\right)^2+\dfrac{17}{4}\le\dfrac{17}{4}\)

Dấu '=' xảy ra khi x=-1 và y=-1/2