Question

Tìm GTNN của các biểu thức sau:

A= 11-10x-x² B= 6x-x²-5

C= 2x-2x²-5 D= (2-x). (x+4)

E= -x²-4x+2 F= 4x-x²+3

G= x²-6x+11 H= 2x²+10x-1

P= 5x+x²

Q= 5x^2-8x-10 I= 9x+3x²

Answer 1

a: \(=-\left(x^2+10x-11\right)\)

\(=-\left(x^2+10x+25-36\right)\)

\(=-\left(x+5\right)^2+36< =36\)

Dấu '=' xảy ra khi x=-5

b: \(=-\left(x^2-6x+5\right)\)

\(=-\left(x^2-6x+9-4\right)\)

\(=-\left(x-3\right)^2+4< =4\)

Dấu '=' xảy ra khi x=3

c: \(=-2\left(x^2-x+\dfrac{5}{2}\right)\)

\(=-2\left(x^2-x+\dfrac{1}{4}+\dfrac{9}{4}\right)\)

\(=-2\left(x-\dfrac{1}{2}\right)^2-\dfrac{9}{2}< =-\dfrac{9}{2}\)

Dấu '=' xảy ra khi x=1/2

d: \(=2x+8-x^2-4x\)

\(=-x^2-2x+8\)

\(=-\left(x^2+2x-8\right)\)

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

\(=-\left(x+1\right)^2+9< =9\)

Dấu '=' xảy ra khi x=-1