Question

What numbers add up to 5 and multiply up to -180 ?

Answer 1

`x+y=5\\ xy=-180\\\\ x=5-y\\ xy=-180\\\\ (5-y)y=-180\\ 5y-y^2+180=0\\ -y^2+5y+180=0\\ \Delta=5^2-4\cdot(-1)\cdot180=25+720=745\\ √(\Delta)=√(745)\\ y_1=(-5-√(745))/(2\cdot(-1))=(5+√(745))/(2)\\ y_2=(-5+√(745))/(2\cdot(-1))=(5-√(745))/(2)\\\\ x_1=5-(5+√(745))/(2)=(10)/(2)-(5+√(745))/(2)=(5-√(745))/(2)\\ x_2=5-(5-√(745))/(2)=(10)/(2)-(5-√(745))/(2)=(5+√(745))/(2)`

These numbers are
`(5+√(745))/(2)` and
`(5-√(745))/(2)`.