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nfndggougou
@nfndggougou
July 2022
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cos2х + cos х – 2 =0. решите плиз
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lsvetik267ls
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1 votes
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amin07am
Verified answer
Cos2x+cosx-2=0
cos²x-sin²x+cosx-2=0
cos²x-(1-cos²x)+cosx-2=0
cos²x-1+cos²x+cosx-2=0
2cos²x+cosx-3=0
Пусть cosx=t , t[-1;1]
2t²+t-3=0
D=1+24=25=5²; 2 корня
t1=(-1+5): 4=1
t2=(-1-5):4=1,5
Обратная замена
cosx=1
x=2Πn; n=Z
3 votes
Thanks 1
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Answers & Comments
Verified answer
Cos2x+cosx-2=0cos²x-sin²x+cosx-2=0
cos²x-(1-cos²x)+cosx-2=0
cos²x-1+cos²x+cosx-2=0
2cos²x+cosx-3=0
Пусть cosx=t , t[-1;1]
2t²+t-3=0
D=1+24=25=5²; 2 корня
t1=(-1+5): 4=1
t2=(-1-5):4=1,5
Обратная замена
cosx=1
x=2Πn; n=Z