Question

[Nguyễn Thành Nam]

giúp mình với

Answer 1

[l҉o҉n҉g҉ d҉z҉]

4a) x² + x + 1 = ( x² + x + 1/4 ) + 3/4 = ( x + 1/2 )² + 3/4 ≥ 3/4 ∀ x

Dấu "=" xảy ra <=> x = -1/2

b) 4x² + 4x - 5 = ( 4x² + 4x + 1 ) - 6 = ( 2x + 1 )² - 6 ≥ -6 ∀ x

Dấu "=" xảy ra <=> x = -1/2

c) ( x - 3 )( x + 5 ) + 4 = x² + 2x - 15 + 4 = ( x² + 2x + 1 ) - 12 = ( x + 1 )² - 12 ≥ -12 ∀ x

Dấu "=" xảy ra <=> x = -1

d) x² - 4x + y² - 8y + 6 = ( x² - 4x + 4 ) + ( y² - 8y + 16 ) - 26 = ( x - 2 )² + ( y - 4 )² - 26 ≥ -26 ∀ x, y

Dấu "=" xảy ra <=> x = 2 ; y = 4

Answer 2

[l҉o҉n҉g҉ d҉z҉]

5a) 2x - x² - 4 = -( x² - 2x + 1 ) - 3 = -( x - 1 )² - 3 ≤ -3 ∀ x

Dấu "=" xảy ra <=> x = 1

b) -x² - 4x = -( x² + 4x + 4 ) + 4 = -( x + 2 )² + 4 ≤ 4 ∀ x

Dấu "=" xảy ra <=> x = -2

c) -9x² + 24x - 18 = -3( x² - 8x + 16 ) + 30 = -3( x - 4 )² + 30 ≤ 30 ∀ x

Dấu "=" xảy ra <=> x = 4

d) 4x - x² - 1 = -( x² - 4x + 4 ) + 3 = -( x - 2 )² + 3 ≤ 3 ∀ x

Dấu "=" xảy ra <=> x = 2

e) 5 - x² + 2x - 4y² - 4y = -( x² - 2x + 1 ) - ( 4y² + 4y + 1 ) + 7 = -( x - 1 )² - ( 2y + 1 )² + 7 ≤ 7 ∀ x, y

Dấu "=" xảy ra <=> x = 1 ; y = -1/2