NHờ mọi người giúp mk
2 câu a,b tính hộ mk những câu còn lại thì tìm x ạ
a) D = x(x + 2) + y(y – 2) – 2xy + 37 khi x-y = 7
b) E = x² + 1/x ² khi x + 1/x =3
c) x² + 4x + 3 = 0
d) x² – 6x + 8 = 0
e) 4x² + 4x – 3 = 0
NHờ mọi người giúp mk
2 câu a,b tính hộ mk những câu còn lại thì tìm x ạ
a) D = x(x + 2) + y(y – 2) – 2xy + 37 khi x-y = 7
b) E = x² + 1/x ² khi x + 1/x =3
c) x² + 4x + 3 = 0
d) x² – 6x + 8 = 0
e) 4x² + 4x – 3 = 0
Đáp án:
a) Ta có: $x(x + 2) + y(y – 2) – 2xy + 37 = (x – y)^{2}+2(x-y)+37=7^2+2.7+37=100$
b) Ta có: $x^2 +\frac{1}{x^2}=(x+\frac{1}{x})^2-2=3^2-2=7$
c) $x^2 + 4x + 3 = 0 \Leftrightarrow (x+1)(x+3)=0\Leftrightarrow $\(\left[ \begin{array}{l}x=-1\\x=-3\end{array} \right.\)
d) $x^{2}-6x+8=0\Leftrightarrow (x-2)(x-4)=0\Leftrightarrow $ \(\left[ \begin{array}{l}x=2\\x=4\end{array} \right.\)
e) $4x^2+4x-3=0\Leftrightarrow (2x-1)(2x+3)=0\Leftrightarrow$\(\left[ \begin{array}{l}x=\frac{1}{2}\\x=\frac{-3}{2}\end{array} \right.\)
`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`
`⇔` \(\left[ \begin{array}{l}2x+3=0\\2x-1=0\end{array} \right.\) `⇔` \(\left[ \begin{array}{l}x=\dfrac{-3}{2}\\x=\dfrac{1}{2}\end{array} \right.\)