Решите уравнение : [tex] \sqrt{(x+1)(2x+3)} =x+3 ;[/tex]. Created by jolieangelina. algebra-ru

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July 2022 1 6 Report

Решите уравнение :
[tex] \sqrt{(x+1)(2x+3)} =x+3 ;[/tex]

Answers & Comments

Voxman $\sqrt{(x+1)(2x+3)} = x+3$

ОДЗ:

$x + 3 \geq 0, \ x \geq -3\\\\
(x+1)(2x+3) \geq 0, \ x \in (-\infty;-\frac{3}{2}] \cup [-1;+\infty)$

$(x+1)(2x+3) = (x + 3)^2\\\\
2x^2 + 5x + 3 = x^2 + 6x + 9\\\\
x^2 - x - 6 = 0\\\\
x^2 - 3x + 2x - 6 = 0\\\\
x(x - 3) + 2(x - 3) = 0\\\\
(x + 2)(x - 3) = 0\\\\
\boxed{\mathbb{OTBET}: \ x_1 = -2, \ x_2 = 3}$

4 votes Thanks 2

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jolieangelina August 2022 | 0 Ответы

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