Rozwiąż równanie.
a)-1/x=x+2
b)9/6-x=x
c)6/x=x+5
d)3/x+2=x
e)2x+4/2x-1=x-1
f)3x+3/x+2=3-x
a)
delta=0
x=-1
b)to jest czy ?
c)
delta = 49
d) tak jak w b)
e)
f)
delta= 16
delta = 0
x = -1
b)
d)
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a)![X^{2}+2x+1=0 X^{2}+2x+1=0](https://tex.z-dn.net/?f=X%5E%7B2%7D%2B2x%2B1%3D0)
delta=0
x=-1
b)to jest
czy
?
c)![x^{2}+5x-6=0 x^{2}+5x-6=0](https://tex.z-dn.net/?f=x%5E%7B2%7D%2B5x-6%3D0)
delta = 49
d) tak jak w b)
e)![2x^{2}-5x-3=0 2x^{2}-5x-3=0](https://tex.z-dn.net/?f=2x%5E%7B2%7D-5x-3%3D0)
delta = 49
f)![-x^{2}-2x+3=0 -x^{2}-2x+3=0](https://tex.z-dn.net/?f=-x%5E%7B2%7D-2x%2B3%3D0)
delta= 16
a)
delta = 0
x = -1
b)![\frac{9}{6-x}=x \\ 6-x\neq0 \\ x \neq6\\ \frac{9}{6-x}-\frac{x}{1}=0\\ \frac{9}{6-x}-\frac{x(6-x)}{6-x}=0\\ \frac{9-6x+x^{2}}{6-x}=0 \\ \frac{9}{6-x}=x \\ 6-x\neq0 \\ x \neq6\\ \frac{9}{6-x}-\frac{x}{1}=0\\ \frac{9}{6-x}-\frac{x(6-x)}{6-x}=0\\ \frac{9-6x+x^{2}}{6-x}=0 \\](https://tex.z-dn.net/?f=%5Cfrac%7B9%7D%7B6-x%7D%3Dx+%5C%5C+6-x%5Cneq0+%5C%5C+x+%5Cneq6%5C%5C+%5Cfrac%7B9%7D%7B6-x%7D-%5Cfrac%7Bx%7D%7B1%7D%3D0%5C%5C+%5Cfrac%7B9%7D%7B6-x%7D-%5Cfrac%7Bx%286-x%29%7D%7B6-x%7D%3D0%5C%5C+%5Cfrac%7B9-6x%2Bx%5E%7B2%7D%7D%7B6-x%7D%3D0+%5C%5C+)
c)![\frac{6}{x}=x+5 \\x\neq0\\ \frac{6}{x}- \frac{x(x+5)}{x}=0\\ \frac{6- x^{2}-5x}{x}=0 \\ -x^{2}-5x+6=0\\ delta = 25-4*6*(-1)=49 \\ \sqrt{49}=7\\ x1=\frac{5-7}{-2}=1\\ x2=\frac{5+7}{-2}=-6 \frac{6}{x}=x+5 \\x\neq0\\ \frac{6}{x}- \frac{x(x+5)}{x}=0\\ \frac{6- x^{2}-5x}{x}=0 \\ -x^{2}-5x+6=0\\ delta = 25-4*6*(-1)=49 \\ \sqrt{49}=7\\ x1=\frac{5-7}{-2}=1\\ x2=\frac{5+7}{-2}=-6](https://tex.z-dn.net/?f=%5Cfrac%7B6%7D%7Bx%7D%3Dx%2B5+%5C%5Cx%5Cneq0%5C%5C+%5Cfrac%7B6%7D%7Bx%7D-+%5Cfrac%7Bx%28x%2B5%29%7D%7Bx%7D%3D0%5C%5C+%5Cfrac%7B6-+x%5E%7B2%7D-5x%7D%7Bx%7D%3D0+%5C%5C+-x%5E%7B2%7D-5x%2B6%3D0%5C%5C+delta+%3D+25-4%2A6%2A%28-1%29%3D49+%5C%5C+%5Csqrt%7B49%7D%3D7%5C%5C+x1%3D%5Cfrac%7B5-7%7D%7B-2%7D%3D1%5C%5C+x2%3D%5Cfrac%7B5%2B7%7D%7B-2%7D%3D-6)
d)![\frac {3}{x+2}=x\\ x+2\neq0\\x\neq-2\\ \frac{3}{x+2}-\frac{x}{1}=0\\ \frac{3}{x+2}-\frac{x(x+2)}{x+2}=0\\ \frac{3-x^{2}-2x}{x+2}=0\\ -x^{2}-2x+3=0\\ delta = 16\\\sqrt{16} =4\\ x1=-3\\x2=1 \frac {3}{x+2}=x\\ x+2\neq0\\x\neq-2\\ \frac{3}{x+2}-\frac{x}{1}=0\\ \frac{3}{x+2}-\frac{x(x+2)}{x+2}=0\\ \frac{3-x^{2}-2x}{x+2}=0\\ -x^{2}-2x+3=0\\ delta = 16\\\sqrt{16} =4\\ x1=-3\\x2=1](https://tex.z-dn.net/?f=%5Cfrac+%7B3%7D%7Bx%2B2%7D%3Dx%5C%5C+x%2B2%5Cneq0%5C%5Cx%5Cneq-2%5C%5C+%5Cfrac%7B3%7D%7Bx%2B2%7D-%5Cfrac%7Bx%7D%7B1%7D%3D0%5C%5C+%5Cfrac%7B3%7D%7Bx%2B2%7D-%5Cfrac%7Bx%28x%2B2%29%7D%7Bx%2B2%7D%3D0%5C%5C+%5Cfrac%7B3-x%5E%7B2%7D-2x%7D%7Bx%2B2%7D%3D0%5C%5C+-x%5E%7B2%7D-2x%2B3%3D0%5C%5C+delta+%3D+16%5C%5C%5Csqrt%7B16%7D+%3D4%5C%5C+x1%3D-3%5C%5Cx2%3D1)
e)![\frac{2x+4}{2x-1}=x-1\\ 2x-1\neq0\\ 2x\neq1\\ x\neq0,5\\ \frac{2x+4}{2x-1}-\frac{x-1}{1}=0\\ \frac{2x+4-((x-1)(2x-1))}{2x-1}=0\\ 2x+4-(2x^{2}-x-2x+1)=0 \\ 2x+4-2x^{2}+3x-1=0\\ -2x^{2}+5x+3=0\\ delta = 49 \\ \sqrt{49}=7 \frac{2x+4}{2x-1}=x-1\\ 2x-1\neq0\\ 2x\neq1\\ x\neq0,5\\ \frac{2x+4}{2x-1}-\frac{x-1}{1}=0\\ \frac{2x+4-((x-1)(2x-1))}{2x-1}=0\\ 2x+4-(2x^{2}-x-2x+1)=0 \\ 2x+4-2x^{2}+3x-1=0\\ -2x^{2}+5x+3=0\\ delta = 49 \\ \sqrt{49}=7](https://tex.z-dn.net/?f=%5Cfrac%7B2x%2B4%7D%7B2x-1%7D%3Dx-1%5C%5C+2x-1%5Cneq0%5C%5C+2x%5Cneq1%5C%5C+x%5Cneq0%2C5%5C%5C+%5Cfrac%7B2x%2B4%7D%7B2x-1%7D-%5Cfrac%7Bx-1%7D%7B1%7D%3D0%5C%5C+%5Cfrac%7B2x%2B4-%28%28x-1%29%282x-1%29%29%7D%7B2x-1%7D%3D0%5C%5C+2x%2B4-%282x%5E%7B2%7D-x-2x%2B1%29%3D0+%5C%5C+2x%2B4-2x%5E%7B2%7D%2B3x-1%3D0%5C%5C+-2x%5E%7B2%7D%2B5x%2B3%3D0%5C%5C+delta+%3D+49+%5C%5C+%5Csqrt%7B49%7D%3D7)
f)![\frac{3x+3}{x+2}=3-x\\ x+2\neq0\\x\neq-2\\ \frac{3x+3}{x+2}-\frac{3-x}{1}=0\\\frac{3x+3-((3-x)(x+2)}{x+2}=0\\ 3x+3-(3x+6-x^{2}-2x)=0\\ x^{2}+2x-3=0\\ delta =16\\ \sqrt16=4\\ x1=1\\x2=-3 \frac{3x+3}{x+2}=3-x\\ x+2\neq0\\x\neq-2\\ \frac{3x+3}{x+2}-\frac{3-x}{1}=0\\\frac{3x+3-((3-x)(x+2)}{x+2}=0\\ 3x+3-(3x+6-x^{2}-2x)=0\\ x^{2}+2x-3=0\\ delta =16\\ \sqrt16=4\\ x1=1\\x2=-3](https://tex.z-dn.net/?f=%5Cfrac%7B3x%2B3%7D%7Bx%2B2%7D%3D3-x%5C%5C+x%2B2%5Cneq0%5C%5Cx%5Cneq-2%5C%5C+%5Cfrac%7B3x%2B3%7D%7Bx%2B2%7D-%5Cfrac%7B3-x%7D%7B1%7D%3D0%5C%5C%5Cfrac%7B3x%2B3-%28%283-x%29%28x%2B2%29%7D%7Bx%2B2%7D%3D0%5C%5C+3x%2B3-%283x%2B6-x%5E%7B2%7D-2x%29%3D0%5C%5C+x%5E%7B2%7D%2B2x-3%3D0%5C%5C+delta+%3D16%5C%5C+%5Csqrt16%3D4%5C%5C+x1%3D1%5C%5Cx2%3D-3)