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anika09
@anika09
July 2022
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Розв’язати рівняння (х+1)/(х^2+х-1) + (х^2+х-1)/(х+1) = 2
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Gerren
(х+1)/(х^2+х-1) + (х^2+х-1)/(х+1) = 2
(х+1)/(х^2+х-1)=a
(х^2+х-1)/(х+1)=1/a
a+1/a=2
a^2+1=2a
a^2-2a+1=0
(a-1)^2=0
a=1
(х+1)/(х^2+х-1)=1
(x+1-x^2-x+1)/(x^2+x-1)=0
2-x^2=0
x^2=2
x=+-√2
2 votes
Thanks 2
anika09
Дуже дякую. Чому я не догадалась? шкода за себе. Дякую.
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Answers & Comments
(х+1)/(х^2+х-1)=a
(х^2+х-1)/(х+1)=1/a
a+1/a=2
a^2+1=2a
a^2-2a+1=0
(a-1)^2=0
a=1
(х+1)/(х^2+х-1)=1
(x+1-x^2-x+1)/(x^2+x-1)=0
2-x^2=0
x^2=2
x=+-√2