a) -( x-y)² - (x-1)² -2 

GTLN = -2

a:

A = 2x - 2xy - 2x^2 - y^2

A = -(x^2 + 2xy + y^2) - (x^2 - 2x + 1) + 1

A = -(x + y)^2 - (x - 1)^2 + 1

Vì (x + y)^2 ≥ 0 ∀ x; y; (x - 1)^2 ≥ 0 ∀ x suy ra:

-(x + y)^2 ≤ 0 và (x - 1)^2 ≤ 0 ∀ x; y

A = -(x + y)^2 - (x - 1)^2 + 1 ≤ 1 ∀ x; y

Dấu bằng xảy ra khi x - 1 = 0 và x + y = 0

x - 1 = 0

x = 1

x + y = 0

y = - x

y = - 1

Vậy Amin = 1 khi x = 1; y = - 1

A = (x^2 + 2x + y^2

a,Ta thấy \(x^2\ge0\) \(\left(\forall x\right)\)

         \(\Rightarrow x^2+2015\ge2015\)

Dấu "=" xảy ra   \(\Leftrightarrow x^2=0\)\(\Rightarrow x=0\)

Vậy Min \(x^2+2015=2015\)\(\Leftrightarrow x=0\)

b, Ta thấy \(\left(1-2x\right)^2\ge0\)\(\left(\forall x\right)\)

      \(\Rightarrow\left(1-2x\right)^2-12\ge-12\)

Dấu "=" xảy ra  \(\Leftrightarrow\)\(\left(1-2x\right)^2=0\)\(\Rightarrow1-2x=0\)\(\Rightarrow2x=0\Rightarrow x=0\)

Vậy Min \(\left(1-2x\right)^2-12=12\Leftrightarrow x=0\)

a) 0

b)-3

c)-1