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

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