Question

What two consecutive numbers have a product of 22952

Answer 1

`x(x+1)=22952\\ \\ x^2+x-22952=0\\ \\ \Delta=1^2-4.1.(-22952)=1+91808=91809\\ \\ x=(-1+√(91809))/(2)=(-1+303)/(2)=(302)/(2)=151`

Numbers are: 151 and 152

Answer 2

`n(n+1)=22952\\ n^2+n-22952=0\\ \Delta=1^2-4\cdot1\cdot(-22952)=91809\\ √(\Delta)=√(91809)=303\\ n_1=(-1-303)/(2\cdot1)=(-304)/(2)=-152\\ n_2=(-1+303)/(2\cdot1)=(302)/(2)=151\\\\ n_1+1=-152+1=-151\\ n_2+1=151+1=152`

Those numbers are -152 and -151 or 151 and 152.