1. Oblicz:
a)( +
)²
b) ( +
)²
2. Oblicz:
a) (1+√2)² + (1-√2)²
b) (2√3 -)²-(2√3 +
)²
c) (2√5-√10)² - (2√5+1)(1-2√5)
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zad.1
a)
b)
zad.2
a)
b)
c)![(2\sqrt{5}-\sqrt{10})^2-(2\sqrt{5}+1)(1-2\sqrt{5})=(2\sqrt{5})^2-2\cdot2\sqrt{5}\cdot \sqrt{10} +(\sqrt{10})^2-(1+2\sqrt{5})(1-2\sqrt{5})=4\cdot5-4\sqrt{50}+10-[1^2-(2\sqrt{5})]=20-4\sqrt{25\cdot2}+10-1+4 \cdot5=20-4\cdot5\sqrt{2}+10-1+20=49-20\sqrt{2} (2\sqrt{5}-\sqrt{10})^2-(2\sqrt{5}+1)(1-2\sqrt{5})=(2\sqrt{5})^2-2\cdot2\sqrt{5}\cdot \sqrt{10} +(\sqrt{10})^2-(1+2\sqrt{5})(1-2\sqrt{5})=4\cdot5-4\sqrt{50}+10-[1^2-(2\sqrt{5})]=20-4\sqrt{25\cdot2}+10-1+4 \cdot5=20-4\cdot5\sqrt{2}+10-1+20=49-20\sqrt{2}](https://tex.z-dn.net/?f=%282%5Csqrt%7B5%7D-%5Csqrt%7B10%7D%29%5E2-%282%5Csqrt%7B5%7D%2B1%29%281-2%5Csqrt%7B5%7D%29%3D%282%5Csqrt%7B5%7D%29%5E2-2%5Ccdot2%5Csqrt%7B5%7D%5Ccdot+%5Csqrt%7B10%7D+%2B%28%5Csqrt%7B10%7D%29%5E2-%281%2B2%5Csqrt%7B5%7D%29%281-2%5Csqrt%7B5%7D%29%3D4%5Ccdot5-4%5Csqrt%7B50%7D%2B10-%5B1%5E2-%282%5Csqrt%7B5%7D%29%5D%3D20-4%5Csqrt%7B25%5Ccdot2%7D%2B10-1%2B4+%5Ccdot5%3D20-4%5Ccdot5%5Csqrt%7B2%7D%2B10-1%2B20%3D49-20%5Csqrt%7B2%7D)