Question

Корень(x+20)-корень(x-1)=3

Answer 1

$sqrt{x+20}-sqrt{x-1}=3; ,; ; ODZ:; ; left { {{x+20geq 0} atop {x-1geq 0}} right. ; left { {{xgeq -20} atop {xgeq 1}} right. ; Rightarrow ; ; xgeq 1\\sqrt{x+20}=3+sqrt{x-1}\\x+20=9+2cdot 3cdot sqrt{x-1}+x-1\\6sqrt{x-1}=12\\sqrt{x-1}=2\\x-1=4\\x=5\\Proverka:; ; sqrt{5+20}-sqrt{5-1}=sqrt{25}-sqrt4=5-2=3; ;; ; 3=3\\Otvet:; ; x=5.$