Question

и

решить уравнение

Answer 1

$1)9^{\frac{1}{x}}+6^{\frac{1}{x}}=2^{\frac{2}{x}+1}\\\\9^{\frac{1}{x}}+6^{\frac{1}{x}} -2*4^{\frac{1}{x}}=0|:4^{\frac{1}{x}}0\\\\(\frac{9}{4})^{\frac{1}{x}}+(\frac{6}{4})^{\frac{1}{x}}-2=0\\\\((\frac{3}{2})^{\frac{1}{x}} )^{2}+(\frac{3}{2})^{\frac{1}{x}}-2=0\\\\(\frac{3}{2})^{\frac{1}{x}}=m,m0\\\\m^{2}+m-2=0 \\\\m_{1}=1\\\\m_{2} =-2$

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

ответ : корней нет

$2)3*16^{x}+2*81^{x}=5*36^{x} \\\\2*81^{x}-5*36^{x}+3*16^{x} =0|:16^{x}0\\\\2*(\frac{9}{4})^{2x}-5*(\frac{9}{4})^{x}+3=0\\\\(\frac{9}{4})^{x}=m,m0\\\\2m^{2}-5m+3=0\\\\D=(-5)^{2}-4*2*3=25-24=1\\\\m_{1}=\frac{5+1}{4}=\frac{3}{2}\\\\m_{2}=\frac{5-1}{4}=1\\\\$

$(\frac{9}{4})^{x} =\frac{3}{2} \\\\(\frac{3}{2})^{2x}=\frac{3}{2}\\\\2x=1\\\\x_{1}=0,5\\\\(\frac{9}{4})^{x}=1\\\\(\frac{9}{4})^{x}=(\frac{9}{4})^{o}\\\\x_{2}=0\\\\Otvet:\boxed{0,5;0}$

Answer 2

ответ и Объяснение по вложении:

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