Question

What are the exact solutions of x2 - 5x - 1 = 0?.

Answer 1

`x^2-5x-1=0\\\\a=1;\ b=-5;\ c=-1\\\Delta=b^2-4ac\\\\\Delta=(-5)^2-4\cdot1\cdot(-1)=25+4=29 \ \textgreater \ 0\\\\therefore\\x_1=(-b-\sqrt\Delta)/(2a)\ and\ (-b+\sqrt\Delta)/(2a)\\\\x_1=(5-√(29))/(2\cdot1)=\boxed{(5-√(29))/(2)}\\\\x_2=(5+√(29))/(2\cdot1)=\boxed{(5+√(29))/(2)}`