1.Rozwiąż równanie;
a)
b)
c)
2.Rozwiąż nierówność:
delta = = 1+2 = 3
x1 =
x2 =
delta = 169 + 4*6*5 = 169+120=289
pierw z delty = 17
2.
ramiona paraboli skierowane do gory
wiec x
ramiona paraboli skierowane do gory wiec
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a)![-\frac{1}{4}x^{2}+x+2=0 -\frac{1}{4}x^{2}+x+2=0](https://tex.z-dn.net/?f=-%5Cfrac%7B1%7D%7B4%7Dx%5E%7B2%7D%2Bx%2B2%3D0)
delta =
= 1+2 = 3
x1 =![\frac{-1-\sqrt{3}}{-\frac{1}{2}} = 2+2\sqrt{3} \frac{-1-\sqrt{3}}{-\frac{1}{2}} = 2+2\sqrt{3}](https://tex.z-dn.net/?f=%5Cfrac%7B-1-%5Csqrt%7B3%7D%7D%7B-%5Cfrac%7B1%7D%7B2%7D%7D+%3D+2%2B2%5Csqrt%7B3%7D)
x2 =![\frac{-1+\sqrt{3}}{-\frac{1}{2}} = 2-2\sqrt{3} \frac{-1+\sqrt{3}}{-\frac{1}{2}} = 2-2\sqrt{3}](https://tex.z-dn.net/?f=%5Cfrac%7B-1%2B%5Csqrt%7B3%7D%7D%7B-%5Cfrac%7B1%7D%7B2%7D%7D+%3D+2-2%5Csqrt%7B3%7D)
b)![(x-3)^{2}+(x-2)^{2}-(x-1)^{2}=0\\ x^{2}-6x+9+x^{2}-4x+4-x^{2}+2x-1=0\\ 3x^{2}-8x+12=0\\ ></p><p> </p><p>delta jest ujemna wiec rownanie nie ma rozwiazan</p><p> </p><p>c)<img src=](https://tex.z-dn.net/?f=%28x-3%29%5E%7B2%7D%2B%28x-2%29%5E%7B2%7D-%28x-1%29%5E%7B2%7D%3D0%5C%5C+x%5E%7B2%7D-6x%2B9%2Bx%5E%7B2%7D-4x%2B4-x%5E%7B2%7D%2B2x-1%3D0%5C%5C+3x%5E%7B2%7D-8x%2B12%3D0%5C%5C)
delta = 169 + 4*6*5 = 169+120=289
pierw z delty = 17
x1 =![\frac{-13-17}{-12}=\frac{-30}{-12}=\frac{5}{2} \frac{-13-17}{-12}=\frac{-30}{-12}=\frac{5}{2}](https://tex.z-dn.net/?f=%5Cfrac%7B-13-17%7D%7B-12%7D%3D%5Cfrac%7B-30%7D%7B-12%7D%3D%5Cfrac%7B5%7D%7B2%7D)
x2 =![\frac{-13+17}{-12}=\frac{4}{-12}=-\frac{1}{3} \frac{-13+17}{-12}=\frac{4}{-12}=-\frac{1}{3}](https://tex.z-dn.net/?f=%5Cfrac%7B-13%2B17%7D%7B-12%7D%3D%5Cfrac%7B4%7D%7B-12%7D%3D-%5Cfrac%7B1%7D%7B3%7D)
2.
a)![(3x-1)^{2}-4(2-x)^{2}>0 \\ 9x^{2}-6x+1-16+16x-4x^{2}>0\\ 5x^{2}+10x-15>0\\ x^{2}+2x-3>0\\ (x-1)(x+3)>0 (3x-1)^{2}-4(2-x)^{2}>0 \\ 9x^{2}-6x+1-16+16x-4x^{2}>0\\ 5x^{2}+10x-15>0\\ x^{2}+2x-3>0\\ (x-1)(x+3)>0](https://tex.z-dn.net/?f=%283x-1%29%5E%7B2%7D-4%282-x%29%5E%7B2%7D%3E0+%5C%5C+9x%5E%7B2%7D-6x%2B1-16%2B16x-4x%5E%7B2%7D%3E0%5C%5C+5x%5E%7B2%7D%2B10x-15%3E0%5C%5C+x%5E%7B2%7D%2B2x-3%3E0%5C%5C+%28x-1%29%28x%2B3%29%3E0)
ramiona paraboli skierowane do gory
wiec x![\in(-\infty;-3)\cup(1;\infty) \in(-\infty;-3)\cup(1;\infty)](https://tex.z-dn.net/?f=%5Cin%28-%5Cinfty%3B-3%29%5Ccup%281%3B%5Cinfty%29)
b)![x^{2}-8x+15\geq-x(2-3x)\geq-3(x+2)\\ x^{2}-8x+15\geq3x^{2}-2x\geq-3x-6\\ 2x^{2}+6x\leq0 \ \ i \ \ 3x^{2}+x+6\geq0\\ 2x(x+3)\leq0 \ \ i \ \ delta \ \ ujemna \ \ wiec \ \ x\in R x^{2}-8x+15\geq-x(2-3x)\geq-3(x+2)\\ x^{2}-8x+15\geq3x^{2}-2x\geq-3x-6\\ 2x^{2}+6x\leq0 \ \ i \ \ 3x^{2}+x+6\geq0\\ 2x(x+3)\leq0 \ \ i \ \ delta \ \ ujemna \ \ wiec \ \ x\in R](https://tex.z-dn.net/?f=x%5E%7B2%7D-8x%2B15%5Cgeq-x%282-3x%29%5Cgeq-3%28x%2B2%29%5C%5C+x%5E%7B2%7D-8x%2B15%5Cgeq3x%5E%7B2%7D-2x%5Cgeq-3x-6%5C%5C+2x%5E%7B2%7D%2B6x%5Cleq0+%5C+%5C+i+%5C+%5C+3x%5E%7B2%7D%2Bx%2B6%5Cgeq0%5C%5C+2x%28x%2B3%29%5Cleq0+%5C+%5C+i+%5C+%5C+delta+%5C+%5C+ujemna+%5C+%5C+wiec+%5C+%5C+x%5Cin+R)
ramiona paraboli skierowane do gory wiec![x\in<-3 \ ; \ 0> x\in<-3 \ ; \ 0>](https://tex.z-dn.net/?f=x%5Cin%3C-3+%5C+%3B+%5C+0%3E)