giúppppppp ahhhhhh

\(F=\left(x-1\right)^2-\left(2x+3\right)^2+5\)

\(=x^2-2x+1-\left(4x^2+12x+9\right)+5\)

\(=-3x^2-14x-3\)

\(=-3\left(x^2+\frac{14}{3}x+\frac{49}{9}\right)+\frac{40}{3}\)

\(=-3\left(x+\frac{7}{3}\right)^2\le0\forall x\) 

Dau '' = '' xay ra \(\Leftrightarrow x=\frac{-7}{3}\)

\(F=\left(x-1\right)^2-\left(2x+3\right)^2+5\)

\(=x^2-2x+1-\left(4x^2+12x+9\right)+5\)

\(=-3x^2-14x-3=-3\left(x^2+\frac{14}{3}x\right)-3\)

\(=-3\left(x^2+2.\frac{7}{3}x+\frac{49}{9}-\frac{49}{9}\right)-3\)

\(=-3\left(x+\frac{7}{3}\right)^2+\frac{40}{3}\le\frac{40}{3}\)

Dấu ''='' xảy ra khi x = -7/3 

Vậy GTLN của F bằng 40/3 tại x = -7/3 

\(A=x^2+2x+9y^2-6y+2018\)

\(=x^2+2x+1+9y^2-6y+1+2016\)

\(=\left(x+1\right)^2+\left(3y-1\right)^2+2016\ge2016\forall x;y\)

Dấu ''='' xảy ra khi x = -1 ; y = 1/3 

Vậy GTNN của A bằng 2016 tại x = -1 ; y = 1/3 

Trời ơi cái quần què gì zậy?!!!!!!!!!!!!!!!!

giải hộ

HOC dot

\(\left(a+b+c\right)^2=a^2+b^2+c^2+2ab+2bc+2ac\)

\(\left(a+b-c\right)^2=a^2+b^2+c^2+2ab-2bc-2ac\) 

\(\left(a-b-c\right)^2=a^2+b^2+c^2-2ab+2bc-2ac\)

\(\left(x-2y+1\right)^2=x^2+4y^2+1-4xy-4y+2x\)

\(\left(3x+y-2\right)^2=9x^2+y^2+4+6xy-12x-4y\)

a) -4x² + 8x - 4

= - (4x² - 8x + 4)

= - (2x - 2)²

b) -x5² + 10 x - 5

= - 5(x² - 2x + 1)

= - 5(x - 1)²

-4x^2+8x-4

=-4.(x^2-2x+1)

=-4.(x-1)^2

31 ) \(-3x^2y^3-6x^3y^2-x^2y^2=-x^2y^2\left(3y-6x+1\right)\)

32 ) \(5x^2y^4-10x^4y^2+5x^2y^2=5x^2y^2\left(y^2-2x+1\right)\)

Thế này á ???

b. Xét vế trái \(\left(a^2+b^2\right)\left(x^2+y^2\right)\)

\(=a^2x^2-2axby+b^2y^2+a^2y^2+2aybx+b^2x^2\)

\(=\left(ax-by\right)^2+\left(ay+bx\right)^2\)(đpcm)

c. Xét vế trái \(a^3-b^3+ab\left(a-b\right)\)

\(=\left(a-b\right)\left(a^2+ab+b^2\right)+ab\left(a-b\right)\)

\(=\left(a-b\right)\left(a^2+2ab+b^2\right)\)

\(=\left(a-b\right)\left(a+b\right)^2\)(đpcm)