Question

Answer 1

a) \(x^2-10x+16=\left(x-5\right)^2-9\ge-9\)

\(ĐTXR\Leftrightarrow x=5\)

b) \(10x-23-x^2=-\left(x-5\right)^2+2\le2\)

\(ĐTXR\Leftrightarrow x=5\)

c) \(x^2+5x-6=\left(x+\dfrac{5}{2}\right)^2-\dfrac{49}{4}\ge-\dfrac{49}{4}\)

\(ĐTXR\Leftrightarrow x=-\dfrac{5}{2}\)

d) \(-x^2-x+1=-\left(x+\dfrac{1}{2}\right)^2+\dfrac{5}{4}\le\dfrac{5}{4}\)

\(ĐTXR\Leftrightarrow x=-\dfrac{1}{2}\)

e) \(2x^2-x-3=2\left(x-\dfrac{1}{4}\right)^2-\dfrac{25}{8}\ge-\dfrac{25}{8}\)

\(ĐTXR\Leftrightarrow x=\dfrac{1}{4}\)

g) \(-3x^2+x+2=-3\left(x-\dfrac{1}{6}\right)^2+\dfrac{25}{12}\le\dfrac{25}{12}\)

\(ĐTXR\Leftrightarrow x=\dfrac{1}{6}\)