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Gortik
@Gortik
August 2022
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[tex] \sqrt{ \frac{x+3}{2}}=x+2[/tex]
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hello93
Привет,
(х+3)/2≥0
х≥-3
возведем обе части в квадрат
(х+3)/2=(х+2)²
х+3=2(х+2)²
х+3=2(х²+4х+4)
х+3=2х²+8х+8
2х²+8х+8-х-3=0
2х²+7х+5=0
D=49-4*2*5=9=3²
х1,2=(-7±3)/4=-1 ; -5/2=-2,5
проверим решение
√(-1+3)/2=-1+2
1=1
√(-2,5+3)/2=-2,5+2
0,5≠-0,5
Ответ: х= -1
2 votes
Thanks 1
Gortik
√(-2,5+3)/2=-2,5+2
Gortik
упс
Gortik
случайно). Спасибо большое.
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Answers & Comments
(х+3)/2≥0
х≥-3
возведем обе части в квадрат
(х+3)/2=(х+2)²
х+3=2(х+2)²
х+3=2(х²+4х+4)
х+3=2х²+8х+8
2х²+8х+8-х-3=0
2х²+7х+5=0
D=49-4*2*5=9=3²
х1,2=(-7±3)/4=-1 ; -5/2=-2,5
проверим решение
√(-1+3)/2=-1+2
1=1
√(-2,5+3)/2=-2,5+2
0,5≠-0,5
Ответ: х= -1