Question

помогите!!!!6 задание

Answer 1

$left { {{x-y=1} atop {81^x-72*9^y=9}} right. left { {{x=y+1} atop {81^{y+1}-72*9^{y}=9}} right. \ \ 81^{y+1}-72*9^{y}=9 \ 81*81^y-72*9^{y}=9 \ 81*(9^y)^2-72*9^{y}-9=0 \ \ 9^y=t, t textgreater 0 \ \81 t^2-72t-9=0 | :9\9t^2-8t-1=0 \ \ D=8^2+4*9=64+36=100=10^2 \ \ t= frac{8+10}{2*9} =1$

$t= frac{8-10}{2*9} =- frac{1}{9} textless 0$ - не удовлетворяет условию t>0

$9^y=t \ 9^y=1 \ 9^y=9^0 \ y=0 \ x=y+1=0+1=1 \ \ OTBET: (1;0)$