Помогите пожалуйста решить!!! Очень-очень срочно!!!

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Secio

03 нояб. 2013 г., 11:46:49 (10 лет назад)

10.50
lg(x-1)=a
3a²-10a+3=0
D=100-36=64, √D=8
a1=(10-8)/6=1/3⇒lg(x-1)=1/3⇒x-1=∛10⇒x=1+∛10
a2=(10+8)/6=3⇒lg(x-1)=3⇒x-1=1000⇒x=1001
10.52
(2+lgx)²+(1+lgx)²=14-lgx
4+2lgx+lg²x+1+2lgx+lg²x-14+lgx=0
2lg²x+7lgx-9=0
lgx=a
2a²+7a-9=0
D=49+72=121, √D=11
a1=(-7-11)/4=-4⇒lgx=-4⇒x=0,0001
a2=(-7+11)/4=1⇒lgx=1⇒x=10
10.54
4lgx-(lg(-x))²=4
ОДЗ  x>0 U -x>0⇒x>0 U x<0- нет решения
10.56
4log²(2)(x-1)+log(2)(x-1)-5=0
log(2)(x-1)=a
4a²+a-5=0
D=1+80=81, √D=9
a1=(-1-9)/8=-5/4⇒log(2)(x-1)=-5/4⇒x-1=2^-5/4=1/2⇒
x=1+1/2
a2=(-1+9)/8=1⇒log(2)(x-1)=1⇒x-1=2⇒x=3
10.58
(log(1/2)4+log(1/2)x)²+log(2)x-log(2)8=8
(log(1/2)x-2)²-2log(1/2)x-3-8=0
log²(1/2) x-4log(1/2)x+4-2log(1/2)x-3-8=0
log²(1/2) x-6log(1/2)x-7=0
log(1/2)x=a
a²-6a-7=0⇒a1+a2=6 U a1*a2=-7
a1=7⇒log(1/2)x=7⇒x=1/128
a2=-1⇒log(1/2)=-1⇒x=2
10.60
(lgx+1)(lgx-1)=3lgx-3
lg²x-1-3lgx+3=0
lg²x-3lgx+2=0
lgx=a
a²-3a+2=0⇒a1+a2=3 U a1*a2=2
a1=2⇒lgx=2⇒x=100
a2=1⇒lgx=1⇒x=10
10.62
(1-4lg²x)/(lgx-2lg²x)=4lgx+5
(1-2lgx)(1+2lgx)/lgx(1-2lgx)=4lgx+5
(1+2lgx)/lgx=4lgx+5
1+lgx=lgx(4lgx+5), x≠√10
4lg²x+5lgx-2lgx-1=0
4lg²x+3lgx-1=0
lgx=a
4a²+3a-1=0
D=9+16=25,√D=5
a1=(-3-5)/8=-1⇒lgx=-1⇒x=0,1
a2=(-3+5)/8=1/4⇒lgx=1/4⇒x=
10.64
(1+log(2)x)²-4log(2)x=0
1+2log(2)x+log²(2)x-4log(2)x=0
1-2log(2)x+log²(2)x=0
(1-log(2)x)²=0
1-log(2)x=0
log(2)x=1
x=2