[tex]zad.8\\
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iloraz~~x~~i~~y\\
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x\div y= \dfrac{x}{y} \\
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\dfrac{2-\sqrt{5} }{2+\sqrt{5} } =\dfrac{2-\sqrt{5} }{2+\sqrt{5} } \cdot \dfrac{2-\sqrt{5} }{2-\sqrt{5} }=\dfrac{(2-\sqrt{5} )^{2} }{2^{2} -(\sqrt{5} )^{2} } =\dfrac{4-4\sqrt{5} +5}{4-5} =\dfrac{9-4\sqrt{5} }{-1} =4\sqrt{5} -9\\
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korzystalam~~ze~~wzorow~~skroconego~~mnozenia:\\
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(x-y)^{2} =x^{2} -2\cdot x \cdot y + y^{2} \\
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(x-y)\cdot (x+y)=x^{2} -y^{2} [/tex]
[tex]zad.55\\
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(x+3)^{2} -(x-3)^{2} -12=x^{2} +6x+9-(x^{2} -6x+9)-12=x^{2} +6x+9-x^{2} +6x-9-12=12x-12\\
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korzystalam~~ze~~wzorow~~skroconego~~mnozenia:\\
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(x+y)^{2} =x^{2} +2xy+y^{2} \\
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(x-y)^{2} =x^{2} -2xy+y^{2} \\
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dla~~x=\sqrt{3} +1\\
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12\cdot (\sqrt{3} +1)-12=12\sqrt{3} +12-12=12\sqrt{3} [/tex]
