45+
![\frac{171x}{137} = \frac{6165+171x}{137}](https://tex.z-dn.net/?f=%20%5Cfrac%7B171x%7D%7B137%7D%20%3D%20%5Cfrac%7B6165%2B171x%7D%7B137%7D%20)
300+x-2x/137=(41100+137x-2x)/137=(41100+135x)/137
![\frac{6165+171x}{137} : \frac{41100+135x}{137} = \frac{6165+171x}{41100+135x}](https://tex.z-dn.net/?f=%20%5Cfrac%7B6165%2B171x%7D%7B137%7D%20%3A%20%5Cfrac%7B41100%2B135x%7D%7B137%7D%20%3D%20%5Cfrac%7B6165%2B171x%7D%7B41100%2B135x%7D%20)
6165+171x=0,2*(41100+135x)
6165+171x=8220+27x
144x=2055
x=2055/144=14
![\frac{13}{48}](https://tex.z-dn.net/?f=%20%5Cfrac%7B13%7D%7B48%7D%20)
Log₂(x+y)+2*log₄(x-y)=5 ОДЗ: x>y x>-y
3^(1+2*log₃(x-y)=48
log₂(x+y)+2*log₂²(x-y)=5
3*3^log₃(x-y)²=48
log₂(x+y)+2*(1/2)*log₂(x-y)=5
3*(x-y)²=48 |÷3
log₂(x+y)+log₂(x-y)=5
(x-y)²=16
1)
log₂((x+y)*(x-y))=5*log₂2
x-y=4
log₂(x²-y²)=log₂2⁵
y=x-4
x²-y²=32
y=x-4
x²-(x-4)²=32
x²-x²+8x-16=32
8x=48 |÷8
x=6 ⇒
y=6-4=2
2)
x²-y²=32
x-y=-4
x²-y²=32
y=x+4
x²-(x+4)²=32
x²-x²-8x-16=32
-8x=48 |÷(-8)
x=-6 ⇒
y=-2 ∉ ОДЗ
<span>Ответ: x=6 y=2.</span>
Решаем методом группировки :