Question

If a expression x + 2374156 × 5374158 is a perfect square, then find the value of x.

Answer 1

Given :  x  +   2374156  * 5374158   is  a perfect square

To find : Value of x

Solution:

x  +   2374156  * 5374158   is  a perfect square

there can be infinite value of x

=> x  +   2374156  * 5374158   = n²

=>  2374156  * 5374158  = n²  - x

=> 2374156  * 5374158 = (n + √x)(n  - √x)

n + √x = 5374158

n  - √x  = 2374156

=> 2√x  = 5374158 - 2374156

=> 2√x  = 3000002

=> √x  =1500001

=> x  =   (1500001)² = 2250003000001

n = 3874157

Another method

x +  2374156  * 5374158   = n²

=> x + (3571986.76)² = n²

=> n = 3571987  ( to get least value of x )

=> x = 3571987²  -  2374156  * 5374158

=> x = 1667521

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