Система уравнений: |--- | 7^2x - 4^2 -45 =0 | |7^x + 4^y -9 =0 |---. Created by CaptainLirov. algebra-ru

Сделаем замену :Ответ : (1 , 0,5)

Система уравнений: |--- | 7^2x - 4^2 -45 =0

CaptainLirov @CaptainLirov

July 2022 1 17 Report

Система уравнений:
|---
| 7^2x - 4^2 -45 =0
|
|7^x + 4^y -9 =0
|---

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Universalka

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Сделаем замену :

$7^{x}=a>0;4^{y}=b>0\\\\\left \{ {{a^{2}-b^{2} =45 } \atop {a+b=9}} \right.\\\\:\left \{ {{(a+b)(a-b)=45} \atop {a+b=9}} \right.\\-------\\\\a-b=5\\\\a=5+b\\\\a+b=9\\\\5+b+b=9\\\\2b=4\\\\b=2\\\\a=9-2=7\\\\7^{x}=7\\\\x=1\\\\4^{y}=2\\\\2^{2y}=2\\\\2y=1\\\\y=0,5$

Ответ : (1 , 0,5)

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