<span>5^2x-5*5^x*2^x-6*2^2x≤0/2^2x
(5/2)^2x-5*(5/2)^x-6≤0
(5/2)^x=a
a²-5a-6≤0
a1+a2=5Ua1*a2=-6⇒a1=-1 U a2=6
-1≤a≤6⇒-1≤(2,5)^x≤6⇒x≤log(2,5)6
x∈(-∞;log(2,5)6]
2
2^x=a
(7-2a)/(a²-12a+32)≥1/4
(28-8a-a²+12a-32)/(a²-12a+32)≥0
(a²-4a+4)/(a²-12a+32)≤0
(a-2)²/(a-4)(a-8)≤0
a=2 a=4 a=8
+ + _ +
------------[2]---------(4)------------(8)----------------------
4<a<8 U a=2
4<2^x<8 U 2^x=2
2<x<3 U x=1
x∈(2;3) U {1}</span>
Х2-2х+1/х2-1=(х-1)2/(х-1)(х+1)=х-1/х+1
5m2+10mn+5n2/15m2-15n2=5(m2+2mn+n2)/15(m-n)(m+n)=(m+n)2/3(m-n)(m+n)=m+n/39m-n)
1)
х-5у=9, х=9+5у,
х²+3ху-у²=3 (9+5у)²+3у(9+5у)-у²=3
81+90у+25у²+27у+15у²-у²-3=0
39у²+117у+78=0
у²+3у+2=0
У1=-1,У2=-2
У1=-1 У2=-2
Х1=9+5·(-1)=4 Х2=9+5·(-2)=-1
Ответ: (4;-1), ( -1;-2)
2)
3х+у=-1, у=-1-3х
х-ху=8 х-х(-1-3х)=8
х+х+3х²-8=0
3х²+2х-8=0
Д=100, Х1= 1 1/3, Х2=-2
Х1=1 1/3 Х2=-2
У1=-1-3·1 1/3=-5 У2=-1-3·(-2)=5
Ответ: (1 1/3;-5),(-2;5)
3)
х+2у=1, х=1-2у
х²-ху-2у²=1 (1-2у)²-у(1-2у)-2у²-1=0,
1-4у+4у²-у+2у²-2у²-1=0
-5у=0
у=0,
х=1-2·0=1
Ответ: (1;0)
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