I am trying to solve this equation where I need the solution of K in term of v
Solve[1 -
K - (54 (20 -
K) v (2 (-10 +
K) (5 (1300 - 10 K + 3 K^2 - 100 (2 + K)) Hypergeometric2F1[
3 - (Sqrt[3] (-10 + K))/Sqrt[(-10 + K)^2],
3 + (Sqrt[3] (-10 + K))/Sqrt[(-10 + K)^2],
1, (-10 + K)/(-20 + K)] + (-13000 + 400 K - 75 K^2 +
6 K^3 + 400 (-25 + 7 K) -
10 (200 - 140 K + 21 K^2)) Hypergeometric2F1[
3 - (Sqrt[3] (-10 + K))/Sqrt[(-10 + K)^2],
3 + (Sqrt[3] (-10 + K))/Sqrt[(-10 + K)^2],
2, (-10 + K)/(-20 + K)]) (((-20 +
K)^3 Hypergeometric2F1[-1 - Sqrt[3], -1 + Sqrt[3],
1, -(10/(-20 + K))])/(-10 + K)^3)))/((12 (-20 + K) (-10 +
K) (5 (1300 - 10 K + 3 K^2 - 100 (2 + K)) Hypergeometric2F1[
3 - (Sqrt[3] (-10 + K))/Sqrt[(-10 + K)^2],
3 + (Sqrt[3] (-10 + K))/Sqrt[(-10 + K)^2],
1, (-10 + K)/(-20 + K)] + (-13000 + 400 K - 75 K^2 +
6 K^3 + 400 (-25 + 7 K) -
10 (200 - 140 K + 21 K^2)) Hypergeometric2F1[
3 - (Sqrt[3] (-10 + K))/Sqrt[(-10 + K)^2],
3 + (Sqrt[3] (-10 + K))/Sqrt[(-10 + K)^2],
2, (-10 + K)/(-20 + K)]) (-(((20 -
K)^3 Hypergeometric2F1[-1 - Sqrt[3], -1 + Sqrt[3],
1, -(K/(-20 + K))])/(8 (-10 + K)^3))) +
1/4 (-3 (-20 + K) (-10 Sqrt[3] - Sqrt[(-10 + K)^2] +
Sqrt[3] K) (-10 Sqrt[3] + Sqrt[(-10 + K)^2] +
Sqrt[3] K) (-K (2 K - 2 (10 + K)) Hypergeometric2F1[
2 - (Sqrt[3] (-10 + K))/Sqrt[(-10 + K)^2],
2 + (Sqrt[3] (-10 + K))/Sqrt[(-10 + K)^2], 1, (
2 (-10 + K))/(-20 + K)] -
2 (K^2 - 2 K (10 + K) +
4 (100 - 10 K + K^2)) Hypergeometric2F1[
2 - (Sqrt[3] (-10 + K))/Sqrt[(-10 + K)^2],
2 + (Sqrt[3] (-10 + K))/Sqrt[(-10 + K)^2], 2, (
2 (-10 + K))/(-20 + K)]) -
2 (-10 +
K)^2 (-K (3 K^2 - 2 K (50 + K) +
4 (300 - 10 K + K^2)) Hypergeometric2F1[
3 - (Sqrt[3] (-10 + K))/Sqrt[(-10 + K)^2],
3 + (Sqrt[3] (-10 + K))/Sqrt[(-10 + K)^2], 1, (
2 (-10 + K))/(-20 + K)] - (10 (-28 + K) K^2 + 3 K^3 +
8 K (1050 - 70 K + K^2) +
16 (-6000 + 750 K - 40 K^2 + K^3)) Hypergeometric2F1[
3 - (Sqrt[3] (-10 + K))/Sqrt[(-10 + K)^2],
3 + (Sqrt[3] (-10 + K))/Sqrt[(-10 + K)^2], 2, (
2 (-10 + K))/(-20 + K)])) )) == 0, K]
But, everytime I am getting a statement Solve::nsmet: This system cannot be solved with the methods available to Solve.
Please give me any suggestion. In have tried to find solution by using 'FindRoot'. But the problem with this is, If I give some value of 'v' then only it gives root.
K
. (Execute? K
) $\endgroup$