Question

giúp em câu 2,3,4,5,6,8 ạ 

Answer 1

2: \(B=-2x^2-8x+5\)

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

\(=-2\left(x^2+4x+4-\dfrac{13}{2}\right)\)

\(=-2\left(x+2\right)^2+13< =13\forall x\)

Dấu '=' xảy ra khi x+2=0

=>x=-2

3: \(C=-x^2+4x+1\)

\(=-x^2+4x-4+5\)

\(=-\left(x^2-4x+4\right)+5=-\left(x-2\right)^2+5< =5\forall x\)

Dấu '=' xảy ra khi x-2=0

=>x=2

4: \(D=x-x^2\)

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

\(=-\left(x-\dfrac{1}{2}\right)^2+\dfrac{1}{4}< =\dfrac{1}{4}\forall x\)

Dấu '=' xảy ra khi \(x-\dfrac{1}{2}=0\)

=>\(x=\dfrac{1}{2}\)

5: \(E=5x-x^2\)

\(=-\left(x^2-5x+\dfrac{25}{4}\right)+\dfrac{25}{4}\)

\(=-\left(x-\dfrac{5}{2}\right)^2+\dfrac{25}{4}< =\dfrac{25}{4}\forall x\)

Dấu '=' xảy ra khi \(x-\dfrac{5}{2}=0\)

=>\(x=\dfrac{5}{2}\)

6: \(G=-5x^2+7x-3\)

\(=-5\left(x^2-\dfrac{7}{5}x+\dfrac{3}{5}\right)\)

\(=-5\left(x^2-2\cdot x\cdot\dfrac{7}{10}+\dfrac{49}{100}+\dfrac{11}{100}\right)\)

\(=-5\left(x-\dfrac{7}{10}\right)^2-\dfrac{11}{20}< =-\dfrac{11}{20}\forall x\)

Dấu '=' xảy ra khi \(x-\dfrac{7}{10}=0\)

=>\(x=\dfrac{7}{10}\)

8: \(K=-9x^2-4y^2+4y-12x+17\)

\(=-\left(9x^2+12x+4\right)-\left(4y^2-4y+1\right)+22\)

\(=-\left(3x+2\right)^2-\left(2y-1\right)^2+22< =22\forall x,y\)

Dấu '=' xảy ra khi \(\left\{{}\begin{matrix}3x+2=0\\2y-1=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=-\dfrac{2}{3}\\y=\dfrac{1}{2}\end{matrix}\right.\)