mk ko bt 123

min=-1 khi x=2

max=5 khi x=-6

cho cách giải luôn đi kê hà my

\(A=\frac{-5}{2x-3x^2-1}\)

\(=\frac{5}{3x^2-2x+1}\)

\(3x^2-2x+1\)

\(=3\left(x^2-\frac23x+\frac13\right)\)

\(=3\left(x^2-2\cdot x\cdot\frac13+\frac19+\frac29\right)=3\left(x-\frac13\right)^2+\frac23\ge\frac23\forall x\)

=>\(A=\frac{5}{3x^2-2x+1}\le5:\frac23=\frac{15}{2}\forall x\)

Dấu '=' xảy ra khi x-1/3=0

=>x=1/3

XD moi x

\(yx^2+y=x^2+3x+5\Leftrightarrow\left(y-1\right)x^2-3x+\left(y-5\right)=0\)

dat y-1=a cho gon

\(ax^2-3x+\left(a-4\right)=0\)(1)

tim DK a de phuong trinh tren(1) co nghiem

a=0=>-3x-4=0=> x=4/3

voi a \(\ne0\)(1) phuong trinh bac 2

=>delta(x)=3^2-4a.(a-4)\(\ge0\) 

\(\Leftrightarrow9-4a^2+16a\ge0\Leftrightarrow4a^2-16a-9\le0\)

delta"(a)=4^2-4.(-9)=16+36=52=4.13

\(\orbr{\begin{cases}a_1=\frac{4-2\sqrt{13}}{4}=1-\frac{\sqrt{13}}{2}\\a_2=\frac{4+2\sqrt{13}}{4}=1+\frac{\sqrt{13}}{2}\end{cases}}\)

\(\left(1-\frac{\sqrt{13}}{2}\right)\le a\le1+\frac{\sqrt{13}}{2}\)

\(1-\frac{\sqrt{13}}{2}\le y-1\le1+\frac{\sqrt{13}}{2}\)

\(2-\frac{\sqrt{13}}{2}\le y\le2+\frac{\sqrt{13}}{2}\)

\(E=\left(2x-5\right)^{10}-12\ge-12\)

Dấu "=" xảy ra \(\Leftrightarrow x=\dfrac{5}{2}\)

Vậy \(E_{min}=-12\Leftrightarrow x=\dfrac{5}{2}\)

\(F=\left(x+5\right)^8+\left|x+5\right|+22\ge22\)

Dấu "=" xảy ra \(\Leftrightarrow x=-5\)

Vậy \(F_{min}=22\Leftrightarrow x=-5\)

\(G=17-\left|3x-2\right|\)

Dấu "=" xảy ra \(x=\dfrac{2}{3}\)

Vậy ​\(G_{max}=17\Leftrightarrow x=\dfrac{2}{3}\)​

\(K=17-\left|3x-2\right|-\left(2-3x\right)^{2020}\le17\)

Dấu "=" xảy ra \(\Leftrightarrow x=\dfrac{2}{3}\)

Vậy \(K_{max}=17\Leftrightarrow x=\dfrac{2}{3}\)