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sayara91
@sayara91
July 2022
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Помогите пожалуйста с примерами)
Решить уравнение x^(lg2)+2^(lgx)=8
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Gerren
x^(lg2)+2^(lgx)=8
x^(ln2/ln10)+2^(lnx/ln10)=8
2^(lnx/ln10)+1)=8
2^(lnx/ln10)=4
2^(lnx/ln10)=2^2
lnx/ln10=2
lnx=2ln10
lnx=ln10^2
x=100
2) 3^x*9^(y^2)=243 3^x*3^2y^2=3^5 3^(x+2y^2)=3^5 x+2y^2=5 x=5-2y^2
lnx+2lny=ln(lg100) lnxy^2=ln2 ln((5-2y^2)y^2)=ln2 x>0 y>0
y^2(5-2y^2)=2
5y^2-2y^4-2=0
2y^4-5y^2+2=0
y^2=a a>0
2a^2-5a+2=0
D=25-16=9 √9=3
a1=(5+3)/4=2
a2=(5-3)/4=2/4=1/2
y^2=2 y^2=1/2
y=√2 y=-√2 искл y=√1/2=√2/2 y=-√1/2 искл
x=5-2*2=1 x=5-1=4
ответ(1;√2) и(4;√2/2)
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Answers & Comments
x^(ln2/ln10)+2^(lnx/ln10)=8
2^(lnx/ln10)+1)=8
2^(lnx/ln10)=4
2^(lnx/ln10)=2^2
lnx/ln10=2
lnx=2ln10
lnx=ln10^2
x=100
2) 3^x*9^(y^2)=243 3^x*3^2y^2=3^5 3^(x+2y^2)=3^5 x+2y^2=5 x=5-2y^2
lnx+2lny=ln(lg100) lnxy^2=ln2 ln((5-2y^2)y^2)=ln2 x>0 y>0
y^2(5-2y^2)=2
5y^2-2y^4-2=0
2y^4-5y^2+2=0
y^2=a a>0
2a^2-5a+2=0
D=25-16=9 √9=3
a1=(5+3)/4=2
a2=(5-3)/4=2/4=1/2
y^2=2 y^2=1/2
y=√2 y=-√2 искл y=√1/2=√2/2 y=-√1/2 искл
x=5-2*2=1 x=5-1=4
ответ(1;√2) и(4;√2/2)