rozwiąż równania

[Mara153]

A) \(x^{2}+5x-2=0\)
B) \(2x^{2}=-8x\)
C) \(\frac{x-2}{3+x}=\frac{2x}{x+1}\)
D) \(|-3|(x+2)^{2}-3(x-3)(x+3)-5x=11\)

[eresh]

A) \(x^{2}\)+5x-2=0

\(x^2+5x-2=0\\
\Delta=25-4\cdot (-2)=33\\
x_1=\frac{-5-\sqrt{33}}{2}\\
x_2=\frac{-5+\sqrt{33}}{2}\)

[eresh]

B)2\(x^{2}\)=-8x

\(2x^2=-8x\\
2x^2+8x=0\\
2x(x+4)=0\\
2x=0\So x=0\\
x+4=0\So x=-4\)

[eresh]

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

\(\frac{x-2}{3+x}=\frac{2x}{x+1}\\
x\neq -3\;\;\; \wedge \;\;\;x\neq -2\\
(x-2)(x+1)=2x(3+x)\\
x^2-x-2=6x+2x^2\\
-x^2-7x-2=0\\
x^2+7x+2=0\\
\Delta=49-4\cdot 2\\
\Delta =41\\
x_1=\frac{-7-\sqrt{41}}{2}\\
x_2=\frac{-7+\sqrt{41}}{2}\)

[eresh]

D)|-3|(x+2)\(^{2}\)-3(x-3)(x+3)-5x=11

\(|-3|(x+2)^2-3(x-3)(x+3)-5x=11\\
3(x+2)^2-3(x-3)(x+3)-5x=11\\
3x^2+12x+12-3x^2+27-5x-11=0\\
7x=-28\\
x=-4
\)