Let x and y be two 2 -digit numbers such that y is obtained by reversing the digits of x . Suppose they also satisfy x²-y²=m² for some positive integer m . The value of x+y+m is.

Step-by-step solution

X a b or x=10 a+by b a or y=10 b+a Now x²-y²=(10 a+b)²-(10 b+a)² array l =99 (a²-b² ) =3² 11(a+b)(a-b) ...... (1) array According of Q(a+b)(a-b)=11 and a-b=1 a+b=11 and a-b=1 a=6, b=5 Hence x=65y=56 and m=33 x+y+m=154