`a,D=x(x+2)+y(y-2)-2xy+37`
`D=x^2+2x+y^2-2y-2xy+37`
`D=(x^2 - 2xy + y^2) + (2x - 2y) + 37`
`D = (x - y)^2 + 2(x - y) + 37`
$\text{Thay x - y = 7 vào D}$
`⇒D = 7^2 + 2 . 7 + 37 = 100`
`b,E=x^2+1/x^2`
`E=x^2+2.x.1/x + 1/x^2 - 2`
`E = (x+1/x)^2 - 2`
$\text{Thay x + $\dfrac{1}{x}$ = 3}$
`⇒E=3^2 - 2 = 7`
`c,x^2+4x+3=0`
`⇔x^2+x+3x+3=0`
`⇔x(x+1)+3(x+1)=0`
`⇔(x+3)(x+1)=0`
`⇔` \(\left[ \begin{array}{l}x+3=0\\x+1=0\end{array} \right.\) `⇔` \(\left[ \begin{array}{l}x=-3\\x=-1\end{array} \right.\)
`d, x^2 - 6x + 8 = 0`
`⇔ x^2 - 4x - 2x + 8 = 0`
`⇔ x(x - 4) - 2(x - 4) = 0`
`⇔ (x - 2)(x - 4) = 0`
`⇔` \(\left[ \begin{array}{l}x-2=0\\x-4=0\end{array} \right.\) `⇔` \(\left[ \begin{array}{l}x=2\\x=4\end{array} \right.\)
`e, 4x^2 + 4x - 3 = 0`
`⇔ 4x^2 + 6x - 2x - 3 = 0`
`⇔ 2x(2x - 1) + 3(2x - 1) = 0`
`⇔ (2x + 3)(2x - 1) = 0`
`⇔` \(\left[ \begin{array}{l}2x+3=0\\2x-1=0\end{array} \right.\) `⇔` \(\left[ \begin{array}{l}x=\dfrac{-3}{2}\\x=\dfrac{1}{2}\end{array} \right.\)
