[tex]9^\frac{1}{x}+6^\frac{1}{x}=2^\frac{2}{x}^+^1[/tex] и [tex]3*16^x+2*81^x=5*36^x[/tex]Решить уравнение. Created by rgolovcov. algebra-ru

tex]Решить уравнение...

rgolovcov @rgolovcov

July 2022 1 16 Report

[tex]9^\frac{1}{x}+6^\frac{1}{x}=2^\frac{2}{x}^+^1[/tex] и [tex]3*16^x+2*81^x=5*36^x[/tex]

Решить уравнение

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$1)9^{\frac{1}{x}}+6^{\frac{1}{x}}=2^{\frac{2}{x}+1}\\\\9^{\frac{1}{x}}+6^{\frac{1}{x}} -2*4^{\frac{1}{x}}=0|:4^{\frac{1}{x}}>0\\\\(\frac{9}{4})^{\frac{1}{x}}+(\frac{6}{4})^{\frac{1}{x}}-2=0\\\\((\frac{3}{2})^{\frac{1}{x}} )^{2}+(\frac{3}{2})^{\frac{1}{x}}-2=0\\\\(\frac{3}{2})^{\frac{1}{x}}=m,m>0\\\\m^{2}+m-2=0 \\\\m_{1}=1\\\\m_{2} =-2$

$(\frac{3}{2})^{\frac{1}{x}}=1\\\\(\frac{3}{2})^{\frac{1}{x}} =(\frac{3}{2})^{o}\\\\\frac{1}{x}=0$

Ответ : корней нет

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