Question

tìm GTLN

A=x² -3x +5

B=\(\dfrac{-5}{x^2-4x+6}\)

C=(a+b+c)(\(\dfrac{1}{a}+\dfrac{1}{b}+\dfrac{1}{c}\)

Answer 1

A=x²-2.\(\dfrac{3}{2}x+\dfrac{9}{4}+\dfrac{11}{4}\)

=\(\left(x-\dfrac{3}{2}\right)^2+\dfrac{11}{4}\ge\dfrac{11}{4}\)

Dau bang xay ra khi x=3/2

Vay GTNN cua A=11/4 khi x=3/2

b) Ta co: x²-4x+6=(x-2)²+2≥2

=> B≥\(-\dfrac{5}{2}\)

Dấu bằng xảy ra khí : x=2

Vay GTNN cua B=-5/2 khi x=2

c) \(\dfrac{1}{a}+\dfrac{1}{b}+\dfrac{1}{c}\ge\dfrac{9}{a+b+c}\left(bdt\right)\)

=> (a+b+c).\(\dfrac{9}{a+b+c}\ge9\)

Dau bang xay ra khi : a=b=c=1/3

Vay GTNN cua C=9 khi a=b=c=1/3