при каких значениях х и у выполняется двойное равенство:
8+√(х-у) = √(х+у) =2√(х²-у²) - √(х-у) - 8
Ответы
Ответ дал:
0
Будет выполнятся, если
![begin{cases}
& text{ } 8+ sqrt{x-y}= sqrt{x+y} \
& text{ } sqrt{x+y}=2 sqrt{x^2-y^2}- sqrt{x-y}-8
end{cases}\ \ begin{cases}
& text{ } 8= sqrt{x+y} - sqrt{x-y} \
& text{ } sqrt{x+y}=2 sqrt{(x-y)(x+y)}- sqrt{x-y}- sqrt{x+y}+ sqrt{x-y} \ & text{ } sqrt{x+y}ne 0
end{cases}\ \ begin{cases}
& text{ } 8= sqrt{x+y}- sqrt{x-y} \
& text{ } sqrt{x+y}(2-2 sqrt{x-y})=0
end{cases}](https://tex.z-dn.net/?f=begin%7Bcases%7D%0A%26amp%3B+text%7B+%7D+8%2B+sqrt%7Bx-y%7D%3D+sqrt%7Bx%2By%7D+++%5C+%0A%26amp%3B+text%7B+%7D++sqrt%7Bx%2By%7D%3D2+sqrt%7Bx%5E2-y%5E2%7D-+sqrt%7Bx-y%7D-8++++%0Aend%7Bcases%7D%5C+%5C+begin%7Bcases%7D%0A%26amp%3B+text%7B+%7D+8%3D+sqrt%7Bx%2By%7D+-+sqrt%7Bx-y%7D++%5C+%0A%26amp%3B+text%7B+%7D++sqrt%7Bx%2By%7D%3D2+sqrt%7B%28x-y%29%28x%2By%29%7D-+sqrt%7Bx-y%7D-+sqrt%7Bx%2By%7D%2B+sqrt%7Bx-y%7D++%5C+%26amp%3B+text%7B+%7D+++sqrt%7Bx%2By%7Dne+0+++%0Aend%7Bcases%7D%5C+%5C+begin%7Bcases%7D%0A%26amp%3B+text%7B+%7D+8%3D+sqrt%7Bx%2By%7D-+sqrt%7Bx-y%7D++%5C+%0A%26amp%3B+text%7B+%7D++sqrt%7Bx%2By%7D%282-2+sqrt%7Bx-y%7D%29%3D0+++%0Aend%7Bcases%7D "begin{cases}
& text{ } 8+ sqrt{x-y}= sqrt{x+y} \
& text{ } sqrt{x+y}=2 sqrt{x^2-y^2}- sqrt{x-y}-8
end{cases}\ \ begin{cases}
& text{ } 8= sqrt{x+y} - sqrt{x-y} \
& text{ } sqrt{x+y}=2 sqrt{(x-y)(x+y)}- sqrt{x-y}- sqrt{x+y}+ sqrt{x-y} \ & text{ } sqrt{x+y}ne 0
end{cases}\ \ begin{cases}
& text{ } 8= sqrt{x+y}- sqrt{x-y} \
& text{ } sqrt{x+y}(2-2 sqrt{x-y})=0
end{cases}")
![begin{cases}
& text{ } 8= sqrt{x+y}- sqrt{x-y} \
& text{ } 1- sqrt{x-y}=0
end{cases}Rightarrowbegin{cases}
& text{ } 8 =sqrt{x+y}- 1 \
& text{ } sqrt{x-y} =1
end{cases}\ \ begin{cases}
& text{ } 9= sqrt{x+y} \
& text{ } sqrt{x-y}=1
end{cases}Rightarrowbegin{cases}
& text{ } 81=x+y \
& text{ } x-y=1
end{cases}Rightarrowbegin{cases}
& text{ } x=81-y \
& text{ } 81-y-y=1
end{cases}](https://tex.z-dn.net/?f=begin%7Bcases%7D%0A%26amp%3B+text%7B+%7D+8%3D+sqrt%7Bx%2By%7D-+sqrt%7Bx-y%7D+++%5C+%0A%26amp%3B+text%7B+%7D+1-+sqrt%7Bx-y%7D%3D0++%0Aend%7Bcases%7DRightarrowbegin%7Bcases%7D%0A%26amp%3B+text%7B+%7D+8+%3Dsqrt%7Bx%2By%7D-+1++%5C+%0A%26amp%3B+text%7B+%7D++sqrt%7Bx-y%7D+%3D1+%0Aend%7Bcases%7D%5C+%5C+begin%7Bcases%7D%0A%26amp%3B+text%7B+%7D+9%3D+sqrt%7Bx%2By%7D++%5C+%0A%26amp%3B+text%7B+%7D++sqrt%7Bx-y%7D%3D1++%0Aend%7Bcases%7DRightarrowbegin%7Bcases%7D%0A%26amp%3B+text%7B+%7D+81%3Dx%2By+%5C+%0A%26amp%3B+text%7B+%7D+x-y%3D1+%0Aend%7Bcases%7DRightarrowbegin%7Bcases%7D%0A%26amp%3B+text%7B+%7D+x%3D81-y+%5C+%0A%26amp%3B+text%7B+%7D+81-y-y%3D1+%0Aend%7Bcases%7D "begin{cases}
& text{ } 8= sqrt{x+y}- sqrt{x-y} \
& text{ } 1- sqrt{x-y}=0
end{cases}Rightarrowbegin{cases}
& text{ } 8 =sqrt{x+y}- 1 \
& text{ } sqrt{x-y} =1
end{cases}\ \ begin{cases}
& text{ } 9= sqrt{x+y} \
& text{ } sqrt{x-y}=1
end{cases}Rightarrowbegin{cases}
& text{ } 81=x+y \
& text{ } x-y=1
end{cases}Rightarrowbegin{cases}
& text{ } x=81-y \
& text{ } 81-y-y=1
end{cases}")
![begin{cases}
& text{ } x=81-y \
& text{ } 2y=80
end{cases}Rightarrowbegin{cases}
& text{ } x=41 \
& text{ } y=40
end{cases}](https://tex.z-dn.net/?f=begin%7Bcases%7D%0A%26amp%3B+text%7B+%7D+x%3D81-y+%5C+%0A%26amp%3B+text%7B+%7D+2y%3D80+%0Aend%7Bcases%7DRightarrowbegin%7Bcases%7D%0A%26amp%3B+text%7B+%7D+x%3D41+%5C+%0A%26amp%3B+text%7B+%7D+y%3D40+%0Aend%7Bcases%7D "begin{cases}
& text{ } x=81-y \
& text{ } 2y=80
end{cases}Rightarrowbegin{cases}
& text{ } x=41 \
& text{ } y=40
end{cases}")
Ответ:
Ответ:
Похожие вопросы
2 года назад
7 лет назад
9 лет назад
9 лет назад
10 лет назад