Question

write the value 'k' of distance between (k,3)and (4,5) is ✓5

Answer 1

Hi ,

(k-4)^2 + (3-5)^2 = 5
(k-4)^2 = 1

taking sq root on both sides
(k - 4)  = +1 or - 1

NOTE: k can have two values here.

so
k = 5
k = 3

Hope it helped.
Let me know if any doubts.

Answer 2

$5 = k ^{2} - 8k + 20$
$k ^{2} - 8k + 15 = 0$
BY FACTORIZATION METHOD
$k ^{2} - 5k - 3k + 15 = 0$
k(k-5)-3(k-5)=0
(k-5)=0 or( k-3)=0
we get k=5 or k=3
THEREFORE, THE VALUE OF K IS 5 & 3