Verified answer

2p/3 = (2√k - 1)/p

2p² = 3(2√k - 1)

2p² = 6√k - 3

2p² + 3 = 6√k

(2p²+3)/6 = √k

k = [(2p²+3)/6]²

Hope this helps

Bye !!

cross multiply

2p^2 = 3[2sqrtk -1]

2p^2 = 6sqrtk - 3

[2p^2 + 3] / 6 = sqrtk

k = [2p^2 + 3]^2 / 36

2 sqrt k -1 = 2p^2 / 3

2sqrt k = (2p^2 + 3) / 3

sqrtk = (2p^2 + 3) / 6

k = (2p^2 +3) ^ 2 / 36

2p/3 = (2√k - 1) / p

=> 2p² = 3(2√k - 1)

=> 2p² = 6√k - 3

=> 2p² + 3 = 6√k

=> (2p²+3)/6 = √k

square both sides, to get

=> k = [(2p²+3)/6]²

Answer

2p^2/3=2sqrtk-1

2p^2/3+1=2sqrtk

2p^2+3

---------- = 2sqrtk

3

2p^2+3

---------- = sqrtk

6

(2p^2+3)^2

-------------- = k

36

cross multiply

you get 2p^2 = 3(2sqrt k -1)

2p^2 = 6sqrtk -3

sqrt k =(2p^2-3)/6

k= (2p^2-3)/6)^2

2p/3 = (2√k - 1) / p

→(2p/3)×p = (2√k - 1)

or (2√k - 1) =2p²/3

or 2√k =2p²/3 +1

and √k =(2p²/3 +1)/2 =(2p² +3)/6

and k = {(2p² +3)/6}²=(2p² +3)²/36

2p/3=(2k^.5-1)/p

...............

2p^2/3 = 2k^.5-1

2p^2/3+1 = 2k^.5

(2p^2+3)/3 = 2k^.5

(2p^2+3)/6 = k^.5

...............

k = (2p^2+3)^2/36

k = (4p^4+12p^2+9)/36

k = p^4/9+p^2/3+.25