Question

Решите пожалуйста уравнение! 16^x-5*36^x+4*81^x=0

Answer 1

$16^x-5cdot36^x+4cdot81^x=0;\ (4^x)^2-5cdot4^xcdot9^x+4cdot(9^x)^2=0;|div (4^x)^2 \ 4cdot( (frac{9}{4} )^x)^2-5(frac{9}{4})^x+1=0;\ (frac{9}{4})^x=t>0;\ 4t^2-5t+1=0;\ D=b^2-4ac=25-16=9=3^2; \ t_{1}= frac{-b-sqrt{D}}{2a}= frac{5-3}{8}= frac{1}{4};\ t_{2}= frac{-b+sqrt{D}}{2a}= frac{5+3}{8}=1;\ (frac{9}{4} )^x= frac{1}{4} \ x=varnoyhing;\ (frac{9}{4})^x=1 ==>x=0$

Answer 2

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