Question

tìm giá trị lớn nhất, giá trị nhỏ nhất:                                                                           A= 3 x^2 + 7x + 8 ; B= x^2 + 2 x + 9 ; C= -3 x^2 + x + 1;   

    D= - x^2 + 7x +9 ; E= 4 x^2 + 8x + 9; F= x^2 + 6 x + y^2 + 8 y+ 9

Answer 1

1: \(A=3x^2+7x+8\)

\(=3\left(x^2+\dfrac{7}{3}x+\dfrac{8}{3}\right)\)

\(=3\left(x^2+2\cdot x\cdot\dfrac{7}{6}+\dfrac{49}{36}+\dfrac{47}{36}\right)\)

\(=3\left(x+\dfrac{7}{6}\right)^2+\dfrac{47}{12}>=\dfrac{47}{12}\)

Dấu '=' xảy ra khi x=-7/6

2: \(=x^2+2x+1+8=\left(x+1\right)^2+8>=8\)

Dấu '=' xảy ra khi x=-1

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

\(=-3\left(x^2-2\cdot x\cdot\dfrac{1}{6}+\dfrac{1}{36}-\dfrac{13}{36}\right)\)

\(=-3\left(x-\dfrac{1}{6}\right)^2+\dfrac{13}{12}< =\dfrac{13}{12}\)

Dấu '=' xảy ra khi x=1/6