Answer
x= -1 or 3
Work Step by Step
To calculate VALUE OF 'x' , we will use distance formula-
r= $ \sqrt { (x_{2} - x_{1}) ^{2} + (y_{2} - y_{1}) ^{2}}$
As per given data
$\sqrt 13$ = $ \sqrt { (1 - x) ^{2} + (5 -2) ^{2}}$
$\sqrt 13$ = $ \sqrt { 1 - 2x +x^{2} + 9 }$
[ on expanding $(1 - x)^{2} $]
$\sqrt 13$ = $ \sqrt { x^{2} - 2x + 10 }$
Squaring both the sides-
13 = $ x^{2} - 2x + 10$
Rearranging-
$ x^{2} - 2x -3$ = 0
Factorizing the L.H.S.-
(x+1) (x-3) = 0
Therefore Either x = -1 or 3
