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ОДЗ:
![left { {{x+1 geq 0} atop {x-7 geq 0}} right. = textgreater left { {{x geq -1} atop {x geq 7}} right. = textgreater x in [7; +infty) left { {{x+1 geq 0} atop {x-7 geq 0}} right. = textgreater left { {{x geq -1} atop {x geq 7}} right. = textgreater x in [7; +infty)](https://tex.z-dn.net/?f=+left+%7B+%7B%7Bx%2B1+geq+0%7D+atop+%7Bx-7+geq+0%7D%7D+right.+++%3D+textgreater+++left+%7B+%7B%7Bx+geq+-1%7D+atop+%7Bx+geq+7%7D%7D+right.++++%3D++textgreater+++x+in+%5B7%3B+%2Binfty%29)
![( sqrt{x+1}- sqrt{x-7})^2=2 ^2 \ \ x+1+x-7-2 sqrt{(x+1)(x-7)}=4 \ 2 sqrt{(x+1)(x-7)}=2x-10 \ 2 sqrt{(x+1)(x-7)}=2(x-5) (:2) \ sqrt{(x+1)(x-7)}=x-5 \ \ (x+1)(x-7)=x^2-10x+25 \ x^2-7x+x-7=x^2-10x+25 \ 4x=32 \ x=8 ( sqrt{x+1}- sqrt{x-7})^2=2 ^2 \ \ x+1+x-7-2 sqrt{(x+1)(x-7)}=4 \ 2 sqrt{(x+1)(x-7)}=2x-10 \ 2 sqrt{(x+1)(x-7)}=2(x-5) (:2) \ sqrt{(x+1)(x-7)}=x-5 \ \ (x+1)(x-7)=x^2-10x+25 \ x^2-7x+x-7=x^2-10x+25 \ 4x=32 \ x=8](https://tex.z-dn.net/?f=%28+sqrt%7Bx%2B1%7D-+sqrt%7Bx-7%7D%29%5E2%3D2+%5E2+%5C++%5C+x%2B1%2Bx-7-2+sqrt%7B%28x%2B1%29%28x-7%29%7D%3D4+%5C++2+sqrt%7B%28x%2B1%29%28x-7%29%7D%3D2x-10+%5C+2+sqrt%7B%28x%2B1%29%28x-7%29%7D%3D2%28x-5%29++%28%3A2%29+%5C++sqrt%7B%28x%2B1%29%28x-7%29%7D%3Dx-5+%5C++%5C+%28x%2B1%29%28x-7%29%3Dx%5E2-10x%2B25+%5C+x%5E2-7x%2Bx-7%3Dx%5E2-10x%2B25+%5C+4x%3D32+%5C+x%3D8)
ОТВЕТ: x=8
ОТВЕТ: x=8
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