Question

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. Find the value of (x + y + m).

Answer 1

2x +2y=2m
2(x+y)=2m
x+y=m

Answer 2

Answer:

,154

Step-by-step explanation:

X  ab or x = 10 a + b

y  ba or y = 10 b + a

Now x2

- y2

= (10a +b)2

- (10 b + a)2

= 99 (a2

- b2)

= 32

x 11(a + b) (a ñ b) ------ (1)

According of Q

(a + b)(a ñ b) = 11 and a ñ b = 1

 a + b = 11 and a ñ b = 1 a = 6, b = 5

Hence

x = 65

y = 56

and m = 33  x + y + m = 154