Question 301484
X^2+(X+2)^2=34
X^2+X^2+4X+4=34
2X^2+4X+4-34=0
2X^2+4X-30=0
2(X^2+2X-15)=0
2(X+5)(X-3)=0
X-3=0
X=3 FOR THE SMALLER INTEGER.
3+2=5 FOR THE LARGER INTEGER.
PROOF:
3^2+5^2=34
9=25=34
34=34
PRODUCT=3*5=15 ANS.