Question

The sum of the squares of two consecutive negative integers is 61. Find the smaller of the two integers

Answer 1

`x^2+(x+1)^2=61\\ x^2+x^2+2x+1-61=0\\ 2x^2+2x-60=0\ \ /:2\\ x^2+x-30=0\\ \Delta=1^2-4\cdot(-40)=1+120=121\ \ \Rightarrow\ \ √(\Delta) =11\\ \\ x_1= (-1-11)/(2) = (-12)/(2) =-6,\ \ \ \ x_2= (-1+11)/(2) = (10)/(2)=5\\ \\Ans.:x=-6`