Question

If x^2 +39 is a perfect square then number of integral values of x is?
(A)2
(B)4
(C)1
(D)8

Answer 1

Given :  x²  + 39   is a perfect Square

To find : number of possible integral values of x

Solution:

x²  + 39   is a perfect Square

Let say x² + 39  = n²

=> n² - x² = 39

=> (n- x)(n+x) = 39

39 = 1 * 39    or    3 * 13

Case 1 :  1 * 39

=> n + x = 39    & n - x = 1

=> n = 20    & x  = 19

19² + 39 = 400 = 20²

Case 2 :  1 * 39

=> n + x =13    & n - x = 3

=> n =8    & x  = 5

5² + 39 = 64 = 8²

Number of integral values of  x  = 2

5 & 19  

Number of integral values of  x  = 2

option  A  is correct

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