Zad. na nudę :
2.
Oblicz: }{-2^3*2^{-2}}](https://tex.z-dn.net/?f=+%5Cfrac%7B%5B+%5Csqrt%7B2+%5Cfrac%7B1%7D%7B4%7D+%7D%2A%28+1%5Cfrac%7B1%7D%7B2%7D%29%5E%7B-1%7D%2B+%5Csqrt%7B2%7D%5D%281-+%5Csqrt%7B2%7D%29+%7D%7B-2%5E3%2A2%5E%7B-2%7D%7D+ "\frac{[ \sqrt{2 \frac{1}{4} }*( 1\frac{1}{2})^{-1}+ \sqrt{2}](1- \sqrt{2}) }{-2^3*2^{-2}}")
2.
Oblicz:
marsuw
 }{-2^3*2^{-2}}= \frac{[ \sqrt{ \frac{9}{4} }*( \frac{3}{2})^{-1}+ \sqrt{2}](1- \sqrt{2}) }{-2^{3-2}} = \frac{(\frac{3}{2}*\frac{2}{3}+\sqrt2)(1- \sqrt{2}) }{-2}=\\ \\= \frac{(1+ \sqrt{2})(1- \sqrt{2})}{-2}= \frac{1^2-(\sqrt2)^2}{-2}= -\frac{1-2}{2}= \frac{1}{2}](https://tex.z-dn.net/?f=+%5Cfrac%7B%5B+%5Csqrt%7B2+%5Cfrac%7B1%7D%7B4%7D+%7D%2A%28+1%5Cfrac%7B1%7D%7B2%7D%29%5E%7B-1%7D%2B+%5Csqrt%7B2%7D%5D%281-+%5Csqrt%7B2%7D%29+%7D%7B-2%5E3%2A2%5E%7B-2%7D%7D%3D+%5Cfrac%7B%5B+%5Csqrt%7B+%5Cfrac%7B9%7D%7B4%7D+%7D%2A%28+%5Cfrac%7B3%7D%7B2%7D%29%5E%7B-1%7D%2B+%5Csqrt%7B2%7D%5D%281-+%5Csqrt%7B2%7D%29+%7D%7B-2%5E%7B3-2%7D%7D+%3D+%5Cfrac%7B%28%5Cfrac%7B3%7D%7B2%7D%2A%5Cfrac%7B2%7D%7B3%7D%2B%5Csqrt2%29%281-+%5Csqrt%7B2%7D%29+%7D%7B-2%7D%3D%5C%5C+%5C%5C%3D+%5Cfrac%7B%281%2B+%5Csqrt%7B2%7D%29%281-+%5Csqrt%7B2%7D%29%7D%7B-2%7D%3D+%5Cfrac%7B1%5E2-%28%5Csqrt2%29%5E2%7D%7B-2%7D%3D+-%5Cfrac%7B1-2%7D%7B2%7D%3D+%5Cfrac%7B1%7D%7B2%7D+++++ "\frac{[ \sqrt{2 \frac{1}{4} }*( 1\frac{1}{2})^{-1}+ \sqrt{2}](1- \sqrt{2}) }{-2^3*2^{-2}}= \frac{[ \sqrt{ \frac{9}{4} }*( \frac{3}{2})^{-1}+ \sqrt{2}](1- \sqrt{2}) }{-2^{3-2}} = \frac{(\frac{3}{2}*\frac{2}{3}+\sqrt2)(1- \sqrt{2}) }{-2}=\\ \\= \frac{(1+ \sqrt{2})(1- \sqrt{2})}{-2}= \frac{1^2-(\sqrt2)^2}{-2}= -\frac{1-2}{2}= \frac{1}{2}")
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jestemt
}{-2^3*2^{-2}} = \frac{[\sqrt{\frac94}*(\frac32)^{-1}+\sqrt2]*(1-\sqrt2)}{-2^{3-2}} = \\\\=\frac{[\frac32*\frac23+\sqrt2](1-\sqrt2)}{-2} = \frac{(1+\sqrt2)(1-\sqrt2)}{-2} = -\frac{1^2-\sqrt2^2}{2} = -\frac{1-2}{2} = \frac12](https://tex.z-dn.net/?f=%5Cfrac%7B%5B%5Csqrt%7B2%5Cfrac14%7D%2A%281%5Cfrac12%29%5E%7B-1%7D%2B%5Csqrt2%5D%281-%5Csqrt2%29%7D%7B-2%5E3%2A2%5E%7B-2%7D%7D+%3D+%5Cfrac%7B%5B%5Csqrt%7B%5Cfrac94%7D%2A%28%5Cfrac32%29%5E%7B-1%7D%2B%5Csqrt2%5D%2A%281-%5Csqrt2%29%7D%7B-2%5E%7B3-2%7D%7D+%3D+%5C%5C%5C%5C%3D%5Cfrac%7B%5B%5Cfrac32%2A%5Cfrac23%2B%5Csqrt2%5D%281-%5Csqrt2%29%7D%7B-2%7D+%3D+%5Cfrac%7B%281%2B%5Csqrt2%29%281-%5Csqrt2%29%7D%7B-2%7D+%3D+-%5Cfrac%7B1%5E2-%5Csqrt2%5E2%7D%7B2%7D+%3D+-%5Cfrac%7B1-2%7D%7B2%7D+%3D+%5Cfrac12 "\frac{[\sqrt{2\frac14}*(1\frac12)^{-1}+\sqrt2](1-\sqrt2)}{-2^3*2^{-2}} = \frac{[\sqrt{\frac94}*(\frac32)^{-1}+\sqrt2]*(1-\sqrt2)}{-2^{3-2}} = \\\\=\frac{[\frac32*\frac23+\sqrt2](1-\sqrt2)}{-2} = \frac{(1+\sqrt2)(1-\sqrt2)}{-2} = -\frac{1^2-\sqrt2^2}{2} = -\frac{1-2}{2} = \frac12")
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