решите уравнение x=2√(2x-5) √(x^4-3x-1)=x^2-1. Created by NRLK3221. algebra-ru

решите уравнение x=2√(2x-5) √(x^4-3x-1)=x^2-1...

NRLK3221 @NRLK3221

July 2022 1 5 Report

решите уравнение x=2√(2x-5)
√(x^4-3x-1)=x^2-1

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$1)\; \; x=2\sqrt{2x-5}\; \; ,\; \; \; ODZ:\; 2x-5\geq 0\; ,\; \; x\geq 2,5\\\\x^2=4\cdot (2x-5)\; \; ,\; \; \; x^2=8x-20\; \; ,\\\\x^2-8x+20=0\; ,\; \; D/4=4^2-20=-4$

$2)\; \; \sqrt{x^4-3x-1}=x^2-1\; \; ,\; \; ODZ:\; \left \{ {{x^4-3x-1\geq 0\; ,} \atop {x^2-1\geq 0\; .}} \right.\\\\x^4-3x-1=(x^2-1)^2\\\\x^4-3x-1=x^4-2x^2+1\\\\2x^2-3x-2=0\; ,\; \; D=9+16=25\; ,\\\\x_1=-\frac{1}{2}\; \; ,\; \; x^2-1=\frac{1}{4}-1=-\frac{3}{4}0} \atop {2^2-1=3>0}} \right. \\\\Otvet:\; \; x=2\; .$

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