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Гулима1
@Гулима1
August 2022
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Lg(x^2+y^2)=1+lg13
Lg(x+y)=lg(x-y)+lg8
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MizoriesKun
G(x²+y²)=1+lg13 ОДЗ х+у >0 ; x-y>0
lg(x+y)=lg(x-y)+lg8
--------------------------------
lg(x²+y²)=lg10+lg13
lg(x+y)=lg(x-y)*8
-----------------------------
lg(x²+y²)=lg130
lg(x+y)=lg(8x- 8y)
----------------------------
x²+y² =130
x+y=8x- 8y
----------------------------
x²+y² =130
7x=9y x=9y/7
(9y/7)²+y² =130
(81y²/49) +y² =130 домножим на 49
81у² +49у²= 6370
130у²=6370
у²=49 ⇒
у₁= 7 х₁=9*7/7 =9
у₂= -7 х₂=-7*9/7 = -9 - эта пара корней не подходит под ОДЗ
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Answers & Comments
lg(x+y)=lg(x-y)+lg8
--------------------------------
lg(x²+y²)=lg10+lg13
lg(x+y)=lg(x-y)*8
-----------------------------
lg(x²+y²)=lg130
lg(x+y)=lg(8x- 8y)
----------------------------
x²+y² =130
x+y=8x- 8y
----------------------------
x²+y² =130
7x=9y x=9y/7
(9y/7)²+y² =130
(81y²/49) +y² =130 домножим на 49
81у² +49у²= 6370
130у²=6370
у²=49 ⇒ у₁= 7 х₁=9*7/7 =9
у₂= -7 х₂=-7*9/7 = -9 - эта пара корней не подходит под ОДЗ