Question

Что нибудь, с решением 11 класс

Answer 1

$4)\left \{ {{2\sqrt{x+y}-3\sqrt{x-y} =3 } \atop {3\sqrt{x+y} +\sqrt{x-y}=10 }|*3} \right.\\\\+\left \{ {{2\sqrt{x+y}-3\sqrt{x-y} =3 } \atop {9\sqrt{x+y}+3\sqrt{x-y}=30 }} \right.\\ 11\sqrt{x+y}=33\\ \sqrt{x+y}=3\\x+y=9\\2*3-3\sqrt{x-y} =3\\3\sqrt{x-y}=3\\\sqrt{x-y}=1\\x-y=1$

$+\left \{ {{x+y=9} \atop {x-y=1}} \right. \\------\\2x=10\\x=5\\y=9-5=4$

ответ : (5 ; 4)

$5)\left \{ {{3^{log_{3}(x-y+1) }=x^{2}-y+1} \atop {log_{\sqrt{21}}(y^{2}-2x)=2}} \right.\\\\\left \{ {{x-y+1=x^{2}-y+1 } \atop {y^{2} -2x=21}} \right.\\\\\left \{ {{x^{2}-x=0 } \atop {y^{2}=21+2x }} \right.\\\\\left \{ {{x(x-1)=0} \atop {y^{2}=21+2x }} \right.$

$x_{1}=0\\\\y^{2}=21+2*0=21\\\\y_{1} =-\sqrt{21}\\\\y_{2}=\sqrt{21}\\\\x_{2}=1\\\\y^{2}=21+2*1=23\\\\y_{3}=-\sqrt{23}\\\\y_{4}=\sqrt{23}$

y₁  и  y₄ - не подходят

ответ : (0 ; - √21) , (1 ; - √23)

6) ОДЗ : x > 0  , x ≠ 1

$log_{x}(x^{2}+4)=log_{x}(5x)\\\\x^{2}+4=5x\\\\x^{2}-5x+4=0\\\\x_{1}=4\\\\x_{2}=1$

x₂ - не подходит

ответ : 4