Question

Решить неравенство
$sqrt{x+8} textgreater x+2$

Answer 1

$sqrt{x+8} textgreater x+2\\1)quad left { {{x+2 textless 0} atop {x+8 geq 0}} right. ; left { {{x textgreater -2} atop {x geq -8}} right. ; ; to ; ; x textgreater -2\\2)quad left { {{x+2 geq 0} atop {x+8 textgreater (x+2)^2}} right. ; left { {{x geq -2} atop {x+8 textgreater x^2+2x+4}} right. left { {{x geq -2} atop {x^2+x-4 textless 0}} right. ; left { {{x geq -2} atop {xin (frac{-1-sqrt{17}}{2},frac{-1+sqrt{17}}{2})}} right. \\frac{-1-sqrt{17}}{2}approx -2,56; ; ;; ; frac{-1+sqrt{17}}{2}approx 1,56$

$xin left [-2,frac{-1+sqrt{17}}{2}right )$