the answer given is 1/4 ((2p^2)/3+1)^2.
2p/3 = (2√k - 1) /
2(p^2)/3 = 2√k - 1
2(p^2)/3 + 1 = 2√k
( 2(p^2)/3 + 1 )/2 = √k
[ ( 2(p^2)/3 + 1 )/2 ]^2 = k
2p/3 = (2sqrt(k) - 1)/p
2p^2/3 = 2sqt(k) - 1
2p^2/3 - 3/3 = 2sqrt(k)
(2p^2 - 3)/3 = 2sqrt(k)
(2p^2 - 3)/6 = sqrt(k)
((2p^2 - 3)/6)^2 = k
(4p^4 - 12p^2 + 9)/36 = k
1/9p^4 - 1/3p^2 + 1/4 = k
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Answers & Comments
2p/3 = (2√k - 1) /
2(p^2)/3 = 2√k - 1
2(p^2)/3 + 1 = 2√k
( 2(p^2)/3 + 1 )/2 = √k
[ ( 2(p^2)/3 + 1 )/2 ]^2 = k
2p/3 = (2sqrt(k) - 1)/p
2p^2/3 = 2sqt(k) - 1
2p^2/3 - 3/3 = 2sqrt(k)
(2p^2 - 3)/3 = 2sqrt(k)
(2p^2 - 3)/6 = sqrt(k)
((2p^2 - 3)/6)^2 = k
(4p^4 - 12p^2 + 9)/36 = k
1/9p^4 - 1/3p^2 + 1/4 = k