Question

the number of pair of two digit square numbers, the sum or difference of which are also square numbers​

Answer 1

Answer:

The two numbers are 16 and 25

16 + 25 = 36 (square of 6)

25 - 16 = 9 (square of 3)

Answer 2

Answer:

suppose 2 digit the number is (10x+y)

reversed number will be (10y+x)

so, adding both the numbers give, 10(x+y) + (x+y) = 11(x+y)

as we know, for a number to be perfect square, each of its prime factors should have an even power and 11 is a prime

Therefore, (x+y) should at least be a multiple of 11.

so, for a two digit number x+y can take only one value 11.

now, the last part is to determine is how many such 2 digit numbers are possible where sum of digits equals to 11.

so, clearly none of the digits can take up a value of 0 or 1.

using permutations and combinations,

the first digit can be filled in 8 ways (namely, 2 to 9)

and the 2nd digit can be filled in only one way as sum if digits is fixed.

Thus, the total number of such 2 digit numbers is equal to 8.

Step-by-step explanation:

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