h(x)=f(x)-2g(x)+1

\(=3x^2-18x+27-2\left|x-3\right|+1\)

\(=3\left(x^2-6x+9\right)-2\left|x-3\right|+1\)

\(=3\left|x-3\right|^2-2\left|x-3\right|+1\)

\(=3\left(\left|x-3\right|^2-\frac23\cdot\left|x-3\right|+\frac13\right)\)

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

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

Dấu '=' xảy ra khi \(\left|x-3\right|-\frac13=0\)

=>\(\left|x-3\right|=\frac13\)

=>\(\left[\begin{array}{l}x-3=\frac13\\ x-3=-\frac13\end{array}\right.\Rightarrow\left[\begin{array}{l}x=3+\frac13=\frac{10}{3}\\ x=3-\frac13=\frac83\end{array}\right.\)

a,Bạn có thể tự làm

b,Có f(x)+g(x)-h(x)=4x^2+3x-2+3x^2-2x+5-5x^2+2x-3=2x^2+3x=x(2x+3)

Để f(x)+g(x)-h(x)=0

thi x(2x+3)=0

suy ra x=0 hoặc x=-3/2

c,f(x)-3x+5=4x^2+3x-2-3x+5=4x^2+3>0 với mọi x

Chúc bạn học tốt!

a) \(f\left(x\right)=4x^2+3x-2\)

\(\Leftrightarrow f\left(\frac{-1}{2}\right)=4.\left(\frac{-1}{2}\right)^2+3.\frac{-1}{2}-2\)

\(\Leftrightarrow f\left(\frac{-1}{2}\right)=4.\frac{1}{4}+\frac{-3}{2}-\frac{4}{2}\)

\(\Leftrightarrow f\left(\frac{-1}{2}\right)=1+\frac{-7}{2}\)

\(\Leftrightarrow f\left(\frac{-1}{2}\right)=\frac{2}{2}+\frac{-7}{2}\)

\(\Leftrightarrow f\left(\frac{-1}{2}\right)=\frac{-5}{2}\)

a,F(-1/2)=4.-1/2^2+3.-1/2-2

=F(-1/2)=-5/2

a)f(x)+h(x)=g(x)=>h(x)=g(x)-f(x)

g(x)-f(x)=(x⁴-x³+x²+5)-(x⁴-3x²+x-1)

           =x⁴-x³+x²+5-x⁴+3x²-x+1

           =(x⁴-x⁴)-x³+(x²+3x²)-x+(5+1)

          =-x³+4x²-x+6

b) f(x)-h(x)=g(x)

=>h(x)=f(x)-g(x)

f(x)-g(x)=(x⁴-3x²+x-1)-(x⁴-x³+x²+5)

          =x⁴-3x²+x-1-x⁴+x³-x²-5

          =(x⁴-x⁴)+x³+(-3x²-x²)+x+(-1-5)

           =x³-4x²+x-6