Question

Rezolvati ecuatia √x+1=5-x in R. Va rog ajutati-ma!!!!

Answer 1

$\sqrt{x+1} =5-x\\ \\ Conditii:~x\geq -1~si~x\leq 5~adica~x\in~[-1,5].\\ \\ Ridici~la~patratos:\\ \\ x+1=(5-x)^2\\ \\ x+1=25+x^2-10x\\ \\ x^2-11x+24=0\\ \\ \Delta=121-96=25=5^2\\ \\ x_1=3\in~[-1,5]\\ \\ x_2=8\notin~[-1,5].\\ \\ Deci,~singura~solutie~este~x=3.~(numar~norocos)$