решите уравнение .................................. Created by Akula17. algebra-ru

решите уравнение ...

Akula17 @Akula17

July 2022 1 9 Report

решите уравнение
.................................

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Artem112

Verified answer

$\sqrt{3x+1}- \sqrt{x+8} =1
\\\
\sqrt{3x+1}= \sqrt{x+8} +1
\\\
3x+1=x+8+1+2 \sqrt{x+8} 
\\\
2x-8=2 \sqrt{x+8} 
\\\
\sqrt{x+8} =x-4
\\\
x+8=x^2-8x+16
\\\
x^2-9x+8=0
\\\
(x-1)(x-8)=0
\\\
x_1=1
\\\
x_2=8$
Проверка:
$\sqrt{3\cdot1+1}- \sqrt{1+8} =2-3 \neq 1
\\\
 \sqrt{3\cdot8+1}- \sqrt{8+8} =5-4 =1
$
Ответ: 8

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