Let the 2-digit number be N=10×a+b, where: a= digit in tens place b= digit in units place P=a×b Formula used: Condition 1: P+a2=84 Condition 2: P+b2=60 Calculations: From (1): P=84−a2 From (2): P=60−b2 ⇒84−a2=60−b2 ⇒24=a2−b2 ⇒(a−b)(a+b)=24 Try factor pairs of 24 : (1,24),(2,12),(3,8),(4,6) Try a−b=2 and a+b=12 ⇒ Add: 2a=14⇒a=7,b=5 Check P=a×b=7×5=35 P+a2=35+49=84 P+b2=35+25=60 N=10×7+5=75 P=35 P+N=35+75=110
