Question

решите систему 11 класс​

Answer 1

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Answer 2

Замена

u=x²+y

v=y-x²

$\left \{ {{u\cdot 2^{v}=1} \atop {9u=6^{-v}}} \right. \\ \\ \left \{ {{u= 2^{-v}} \atop {u=6^{-v}\cdot\frac{1}{9}}} \right. \\ \\ 2^{-v}=6^{-v}\cdot3^{-2}\\ \\2^{-v}=3^{-v}\cdot2^{-v}\cdot3^{-2} \\ \\ 1=3^{-v-2}\Rightarrow -v-2=0\\ \\ v=-2\\ \\ u=2^{-(-2)}=4$

$\left \{ {{x^2+y=4} \atop {y-x^2=-2}} \right.$

Складываем

2y=2

y=1

x²=3

x=±√3

О т в е т. (-√3;1); (√3;1)