Question

Answer 1

Bài 3

a) (x² - 1)(x + 1) - x²(x + 2) + x² = 21

x³ + x² - x - 1 - x³ - 2x² + x² = 21

-x + 1 = 21

x = 1 - 21

x = -20

b) (2x + 3)² - (3x - 2)² = 0

(2x + 3 - 3x + 2)(2x + 3 + 3x - 2) = 0

(-x + 5)(5x + 1) = 0

-x + 5 = 0 hoặc 5x + 1 = 0

*) -x + 5 = 0

x = 5

*) 5x + 1 = 0

5x = -1

x = -1/5

Vậy x = -1/5; x = 5

Answer 2

3:

a: \(\left(x^2-1\right)\left(x+1\right)-x^2\left(x+2\right)+x^2=21\)

=>\(x^3+x^2-x-1-x^3-2x^2+x^2=21\)

=>-x-1=21

=>-x=22

=>x=-22

b: \(\left(2x+3\right)^2-\left(3x-2\right)^2=0\)

=>\(\left(2x+3+3x-2\right)\left(2x+3-3x+2\right)=0\)

=>\(\left(5x+1\right)\left(5-x\right)=0\)

=>\(\left[{}\begin{matrix}x=-\dfrac{1}{5}\\x=5\end{matrix}\right.\)

4:

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

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

\(=-\left(x^2-x+\dfrac{1}{4}+\dfrac{3}{4}\right)\)

\(=-\left(x-\dfrac{1}{2}\right)^2-\dfrac{3}{4}< =-\dfrac{3}{4}\)

Dấu = xảy ra khi x-1/2=0

=>x=1/2

Answer 3

Bài 4

A = x - x² - 1

= -(x² - x + 1)

= -(x² - 2.x.1/2 + 1/4 + 3/4)

= -(x - 1/2)² - 3/4

Do (x - 1/2)² ≥ 0 với mọi x ∈ R

⇒ -(x - 1/2)² ≤ 0 với mọi x ∈ R

⇒ -(x - 1/2)² - 3/4 ≤ -3/4 với mọi x  ∈ R

Vậy GTLN của A là -3/4 khi x = 1/2