Предмет: Алгебра, автор: Аноним

Решить уравнения

1)  sqrt{ frac{1}{1-x}+ frac{1}{x}  } =  frac{2}{ sqrt{1-x} }


2) 2 sqrt{x+1}- frac{4}{ sqrt{x+1} }+7=0

Ответы

Автор ответа: Матов
0
1) \
sqrt{frac{1}{1-x}+frac{1}{x}}=frac{2}{sqrt{1-x}}\
x neq 1\
x<1\\
 sqrt{frac{1}{x-x^2}}=sqrt{frac{4}{1-x}}\
frac{1}{x-x^2}=frac{4}{1-x}\
frac{1}{x-x^2}=frac{4x}{x-x^2}\
x=frac{1}{4}

2)\
2sqrt{x+1}-frac{4}{sqrt{x+1}}+7=0\
2(x+1)+7sqrt{x+1}-4=0\
x neq -1\
x<-1\\
sqrt{x+1}=t\
x+1=t^2\
2t^2+7t-4=0\
D=49+4*2*4=9^2\
 t=frac{1}{2}\
 t=-4<0\
x+1=frac{1}{4}\
x=-frac{3}{4}
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