Question

Find the two consecutive natural numbers whose squares have the sum 181

Answer 1

Let the first number be X ,then the next number is X+1
as per the question

X2+(X+1)2=181
X2+X2+2x+1=181
2X2+2x+1 = 181
2x2+2x-180=0
dividing the equation by 2 ,we get
X2+X-90=0
applying factorisation
(X+10)(X-9)=0
then X=-10 or X=9
If X=-10 ,then it's consecutive number is -9
let us check this by putting values in equation X2+(X+1)2=181
(-10)2+(-9)2=100+81=181
this is correct
next put the value X=9 and X+1=10
(9)2+(10)2=181
this is also correct .