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July 2022 1 20 Report

ИРРАЦИОНАЛЬНЫЕ УРАВНЕНИЯ И НЕРАВЕНСТВА
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[tex]1) \sqrt{1-2x} = 7

2) \sqrt{3+2x} = x[/tex]

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NNNLLL54

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$1)\quad \sqrt{1-2x}=7\; ,\; \; \; ODZ:\; \; 1-2x \geq 0\; ,\; \; x \leq \frac{1}{2}\\\\1-2x=49\\\\2x=-48\\\\x=-24\; \; -\; \; otvet\\\\\\2)\quad \sqrt {3+2x}=x\; ,\; \; \; ODZ:\; x \geq 0\\\\3+2x=x^2\\\\x^2-2x-3=0\\\\x_1=-1\; ,\; \; x_2=3\; \; (teorema\; Vieta)\\\\x_1=-1\notin ODZ\\\\Otvety:\; \; x=3\; .$

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