Find two consecutive positive integers such that the sum of their squares is 181
consecutive positive integers: x and x+1
(x)²+(x+1)²= 181
x² +( x² +2x +1) =181 (expanded (x+1)²)
2x²+2x+1=181 (simplified)
2x²+2x+1-181=181-181 (subtraction property)
2x²+2x-180=0
Factor to solve for x
2x²+2x-180=0
2(x+10)(x-9)=0
2≠0
x+10=0
x+10-10=0-10
x=-10 number must be a positive integer, cannot use -10
x-9=0
x-9+9=0+9
x=9 we can use this one, it is positive
x=9 and x+1=9+1=10
two consecutive positive integers such that the sum of their squares is 181 are:
9 and 10
9²+10²=181
81+100=181
181=181
