Х=-8/у
(х-4)(у-2)=-12
(-8/у-4)(у-2)=-12
-8+16/у-4у+8=-12
16/у-4у=-12
16-4у²=-12у
4у²-12у-16=0
Д=(-12)²-4*4*(-16)=144+256=400=20²
х1=20+12 / 2*4 =32/8=4
х2=20-12 / 2*4 =8/8=1
1
a)4-1+3=6
b)2log(7)16/[log(3)(10-1)*log(7)2]=2*4log(2)7/[log(3)9*log(7)2]=8/log(3)9=8/2=4
2
a)2^x=t
t²-3t+2=0
t1+t2=3 U t1*t2=2
t1=1⇒26x=1⇒x=0
t2=2⇒26x=2⇒x=1
b)log(20x+6(log(2)x)/2=8
log(20x+3log(2)x=8
4log(2)x=8
log(2)x=2
x=4
3
a)3^x*(3²-2*3+1)<12
4*3^x<12
3^x<3
x<1
x∈(-∞;1)
b)x>0
log(0,5)x=t
t²+3t-4≤0
t1+t2=-3 U t1*t2=-4
t1=-4 U t2=1
-4≤t≤1
{log(0,5)x≥-4⇒x≤16
{log(0,5)x≤1⇒x≥1/2
x∈[1/2;16]
6
5*6/5*(5/6)^x-9*(5/6)^-x +3=0
(5/6)6x=t
6t-9/t +3=0
6t²+3t-9=0
2t²+t-3=0
D=1+24=25
t1=(-1-5)/4=-3/2⇒(5/6)^x=-3/2 нет решения
t2=(-1+5)/4=1⇒(5/6)^x=1⇒x=0
16/40=4/10=2/5=0.4
57/76=3/4=0.75
(27*14)/(35*15)=9*2 / 5*5=0.72
Ab + ac + ad + bx + cx + dx = a*(b+c+d)+x*(b+c+d)=(a+x)*(b+c+d)
{х+у=5
{x-y²=3
{у=5-х
{х-(5-х)²=3
х-(5-х)²=3
х-(25-10х+х²)=3
х-25+10х-х²-3=0
-х²+11х-28=0 | ·(-1)
х²-11х+28=0
D=b²-4ac
D=121-4×28=9, √D=3
x¹,²=-B±√D/2a
x1=11-3/2=4
x2=11+3/2=7
у1=5-4=1
у2=5-7=-2
Ответ: (4;1),(7;-2)