Pięć przykładów do obliczenia z matematyki:P Pilne!
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2.![\sqrt{61+\sqrt{11-\sqrt[3]{8}}} = \sqrt{61+\sqrt{11-2}} = \sqrt{61+\sqrt{9}} = \sqrt{61+ 3} = \\ =\sqrt{64} = 8 \sqrt{61+\sqrt{11-\sqrt[3]{8}}} = \sqrt{61+\sqrt{11-2}} = \sqrt{61+\sqrt{9}} = \sqrt{61+ 3} = \\ =\sqrt{64} = 8](https://tex.z-dn.net/?f=%5Csqrt%7B61%2B%5Csqrt%7B11-%5Csqrt%5B3%5D%7B8%7D%7D%7D+%3D+%5Csqrt%7B61%2B%5Csqrt%7B11-2%7D%7D+%3D+%5Csqrt%7B61%2B%5Csqrt%7B9%7D%7D+%3D+%5Csqrt%7B61%2B+3%7D+%3D+%5C%5C+%3D%5Csqrt%7B64%7D+%3D+8)
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5.![\frac{5^{2011}-5^{2010}}{\sqrt{7} + \sqrt[3]{(-1)}} = \frac{5\cdot 5^{2010}-5^{2010}}{\sqrt{7} -1} = \frac{5^{2010}(5 - 1)}{\sqrt{7} -1} = \frac{5^{2010} \cdot 4 \cdot (\sqrt{7} + 1)}{(\sqrt{7} -1)(\sqrt{7} + 1)} = \\ = \frac{5^{2010} \cdot 4 \cdot (\sqrt{7} + 1)}{7 - 1} = \frac{5^{2010} \cdot 4 \cdot (\sqrt{7} + 1)}{6} =\frac{5^{2010} \cdot 2 \cdot (\sqrt{7} + 1)}{3} =\frac{5^{2010} \cdot (2\sqrt{7} + 2)}{3} \frac{5^{2011}-5^{2010}}{\sqrt{7} + \sqrt[3]{(-1)}} = \frac{5\cdot 5^{2010}-5^{2010}}{\sqrt{7} -1} = \frac{5^{2010}(5 - 1)}{\sqrt{7} -1} = \frac{5^{2010} \cdot 4 \cdot (\sqrt{7} + 1)}{(\sqrt{7} -1)(\sqrt{7} + 1)} = \\ = \frac{5^{2010} \cdot 4 \cdot (\sqrt{7} + 1)}{7 - 1} = \frac{5^{2010} \cdot 4 \cdot (\sqrt{7} + 1)}{6} =\frac{5^{2010} \cdot 2 \cdot (\sqrt{7} + 1)}{3} =\frac{5^{2010} \cdot (2\sqrt{7} + 2)}{3}](https://tex.z-dn.net/?f=%5Cfrac%7B5%5E%7B2011%7D-5%5E%7B2010%7D%7D%7B%5Csqrt%7B7%7D+%2B+%5Csqrt%5B3%5D%7B%28-1%29%7D%7D+%3D+%5Cfrac%7B5%5Ccdot+5%5E%7B2010%7D-5%5E%7B2010%7D%7D%7B%5Csqrt%7B7%7D+-1%7D+%3D+%5Cfrac%7B5%5E%7B2010%7D%285+-+1%29%7D%7B%5Csqrt%7B7%7D+-1%7D+%3D+%5Cfrac%7B5%5E%7B2010%7D+%5Ccdot+4+%5Ccdot+%28%5Csqrt%7B7%7D+%2B+1%29%7D%7B%28%5Csqrt%7B7%7D+-1%29%28%5Csqrt%7B7%7D+%2B+1%29%7D+%3D+%5C%5C+%3D+%5Cfrac%7B5%5E%7B2010%7D+%5Ccdot+4+%5Ccdot+%28%5Csqrt%7B7%7D+%2B+1%29%7D%7B7+-+1%7D+%3D+%5Cfrac%7B5%5E%7B2010%7D+%5Ccdot+4+%5Ccdot+%28%5Csqrt%7B7%7D+%2B+1%29%7D%7B6%7D+%3D%5Cfrac%7B5%5E%7B2010%7D+%5Ccdot+2+%5Ccdot+%28%5Csqrt%7B7%7D+%2B+1%29%7D%7B3%7D+%3D%5Cfrac%7B5%5E%7B2010%7D+%5Ccdot+%282%5Csqrt%7B7%7D+%2B+2%29%7D%7B3%7D+)