Question

Решите уравнение
x/(√(x+1) +1)=√(x+10) -4

Answer 1

$\frac{x}{\sqrt{x+1}+1}=\sqrt{x+10}-4\\\sqrt{x+1}=a;\sqrt{x+10}=b\\x-b\left ( a+1 \right )+4\left ( a+1 \right )=0\\x=ab-4a+b-4\\\sqrt{x+1}=a\Leftrightarrow x=a^2-1\\b\left ( a+1 \right )-a^2-4a-3=0\\b\left ( a+1 \right )-\left ( a+1 \right )\left ( a+3 \right )=0\\\left ( b-a-3 \right )\left ( a+1 \right )=0\\a\geq 0\Rightarrow a=b-3\Rightarrow b\left ( b-3 \right )-4\left ( b-3 \right )-b^2+b-6=0\\b^2-7b+12+b+6-b^2=0\Leftrightarrow 6b=18\Rightarrow b=3\Rightarrow x=-1$