Question

X^2+9x+7 Tìm GTNN

Answer 1

\(x^2+9x+7=x^2+2.\dfrac{9}{2}+\dfrac{81}{4}-\dfrac{81}{4}+7\)

\(=\left(x+\dfrac{9}{2}\right)^2-\dfrac{53}{4}\ge-\dfrac{53}{4}\)

Dấu ''='' xảy ra khi x = -9/2 

Vậy GTNN biểu thức bằng -53/4 tại x = -9/2 

Answer 2

\(x^2+9x+7\)

\(=x^2+2\cdot x\cdot\dfrac{9}{2}+\dfrac{81}{4}-\dfrac{53}{4}\)

\(=\left(x+\dfrac{9}{2}\right)^2-\dfrac{53}{4}\ge-\dfrac{53}{4}\forall x\)

Dấu '=' xảy ra khi \(x=-\dfrac{9}{2}\)