<em>О</em><em>т</em><em>в</em><em>е</em><em>т</em><em>:</em><em> </em><em>9</em>
1. (х+4)²+х²=2х-1
х²+8х+16+х²=2х-1
2х²+8х-2х+16+1=0
2х²+6х+17=0
D=36+4×2×17=172=2кореньиз43
х1=(-6+2кореньиз43)/4= - (3+кореньиз43)/2
х2=(-6-2кореньиз43)/4= - (3-кореньиз43)/2
2. х(х²-2х)=х³-8
х²(х-2)=(х-2)(х²+2х+4)
х²=х²+2х+4
2х+4=0
2х=-4
х=-2
3. (х+5)(х-4)+х²+18=0
х²-4х+5х-20+х²+18=0
2х²+х-2=0
D=1+4×2×2=17
х= (-1±кореньиз17)/4
4. (х+7)(х-7)+(х-3)²=53
х²-49+х²-6х+9=53
2х²-6х-40-53=0
2х²-6х-93=0
D=36+4×2×93=36+744=780=2кореньиз195
х= (6±2кореньиз195)/4= (3±кореньиз195)/2
1/3х = 12
х = 12 : 1/3
х = 36
1/3 * 36 = 12
12 = 12
Сначала мы логарифмируем, опуская степень вниз:
lgx*(9lg^3(x)-11lg(x))=lg0,01;
Т.к. lg0,01=log10(0,01)=log10(1/100)=log10(10)^-2=-2;Т.к. loga(a)^r=r;
9lg^4(x)-11lg^2(x)=-2;
Делаем замену, lg^2(x)=y;
9y^2-11y+2=0;
D=49;
y1=1;
y2=2/9;
Возвращаемся в замену:
lg^2(x)=1;
lgx=1;
x=10;
lgx=-1;
x=10^-1;
x=1/10;
lg^2(x)=2/9;
<span><span><span><span><em><span><span>lgx=<span><span><span><span><em><span><span>+/-<span><span><span><span><em><span><span>√</span></span></em></span></span></span></span>2/3;</span></span></em></span></span></span></span></span></span></em></span></span></span></span>
<span><span><span><span><em><span><span>lgx=<span><span><span><span><em><span><span>√</span></span></em></span></span></span></span>2/3;</span></span></em></span></span></span></span>
<span><span><span><span><em><span><span>x=10^(<span><span><span><span><em><span><span>√</span></span></em></span></span></span></span>2/3);</span></span></em></span></span></span></span>
<span><span><span><span><em><span><span>lgx=-<span><span><span><span><em><span><span>√</span></span></em></span></span></span></span>2/3;</span></span></em></span></span></span></span>
<span><span><span><span><em><span><span>x=10^(-<span><span><span><span><em><span><span>√</span></span></em></span></span></span></span>2/3);</span></span></em></span></span></span></span>
<span><span><span><span><em><span><span>Ответ:</span></span></em></span></span></span></span>
<span><span><span><span><em><span><span>x=10;x=1/10;x=10^(<span><span><span><span><em><span><span>√</span></span></em></span></span></span></span>2/3);x=10^(-<span><span><span><span><em><span><span>√</span></span></em></span></span></span></span>2/3);
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