Решите уравнение (9x^2+6x-3)*корень из 9x^2+18x+5=0. Created by 6603673. algebra-ru

Решите уравнение (9x^2+6x-3)*корень из 9x^2+18x+5=0...

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Решите уравнение
(9x^2+6x-3)*корень из 9x^2+18x+5=0

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$(9x^2+6x+3)\cdot \sqrt{9x^2+18x+5}=0\; ,\\\\ ODZ:\; \; 9x^2+18x+5 \geq 0\; ,\\\\9x^2+18x+5=0\; ,\; D/4=81-45=36,\\\\ x_1=\frac{-9-6}{9}=-\frac{5}{3},\; x_2=\frac{-9+6}{9}=-\frac{1}{3}\\\\+++(-\frac{5}{3})---(-\frac{1}{3})+++\\\\x\in (-\infty ,-\frac{5}{3}\, ]\cup [\, -\frac{1}{3},+\infty )\\\\a)\; 9x^2+6x+3=0\; ,\; \; D/4=9-9\cdot 3=-18\ \textless \ 0\; \to \; x\in \varnothing \\\\b)\; \sqrt{9x^2+18x+5}=0\; ,\; \; x_1=-\frac{5}{3}\; ,\; \; x_2=-\frac{1}{3}$

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