Question

решить уравнение √(4-x)-√(5+x)=3

Answer 1

$sqrt{4-x}-sqrt{5+x}=3\O.D.3.:\begin{cases}4-xgeq0\5+xgeq0end{cases}Rightarrowbegin{cases}xleq4\xgeq-5end{cases}Rightarrow xin[-5;;4]\sqrt{4-x}=sqrt{5+x}+3\4-x=5+x+6sqrt{5+x}+9\6sqrt{5+x}=4-x-5-x-9\6sqrt{5+x}=-10-2x\3sqrt{5+x}=-5-x\9(5+x)=25+10x+x^2\x^2+10x+25-45-9x=0\x^2+x-20=0\D=1+4cdot20=81\x_{1,2}=frac{-1pm9}2\x_1=-5,;x_2=4$