matzeros=(({{-1, 1, \[Placeholder], 1, 1, 1, \[Placeholder], 0, 0, \[Placeholder], \[Placeholder], 0, 0, \[Placeholder], \[Placeholder]}, {1, -1, 1, 1, \[Placeholder], 1, \[Placeholder], 0, \[Placeholder], 0, \[Placeholder], \[Placeholder], 0, 0, \[Placeholder]}, {\[Placeholder], 1, -1, 1, \[Placeholder], \[Placeholder], 1, \[Placeholder], \[Placeholder], 0, 0, \[Placeholder], \[Placeholder], 0, \[Placeholder]}, {1, 1, 1, -1, 1, \[Placeholder], 1, 0, 0, 0, 0, \[Placeholder], \[Placeholder], \[Placeholder], 0}, {1, \[Placeholder], \[Placeholder], 1, -1, 1, \[Placeholder], \[Placeholder], 0, \[Placeholder], \[Placeholder], 0, \[Placeholder], \[Placeholder], 0}, {1, 1, \[Placeholder], \[Placeholder], 1, -1, 1, \[Placeholder], \[Placeholder], \[Placeholder], \[Placeholder], 0, 0, 0, 0}, {\[Placeholder], \[Placeholder], 1, 1, \[Placeholder], 1, -1, \[Placeholder], \[Placeholder], \[Placeholder], 0, \[Placeholder], \[Placeholder], 0, 0}, {0, 0, \[Placeholder], 0, \[Placeholder], \[Placeholder], \[Placeholder], -1, 1, 1, \[Placeholder], \[Placeholder], 1, \[Placeholder], \[Placeholder]}, {0, \[Placeholder], \[Placeholder], 0, 0, \[Placeholder], \[Placeholder], 1, -1, \[Placeholder], \[Placeholder], 1, \[Placeholder], \[Placeholder], 1}, {\[Placeholder], 0, 0, 0, \[Placeholder], \[Placeholder], \[Placeholder], 1, \[Placeholder], -1, 1, \[Placeholder], \[Placeholder], 1, \[Placeholder]}, {\[Placeholder], \[Placeholder], 0, 0, \[Placeholder], \[Placeholder], 0, \[Placeholder], \[Placeholder], 1, -1, \[Placeholder], \[Placeholder], 1, 1}, {0, \[Placeholder], \[Placeholder], \[Placeholder], 0, 0, \[Placeholder], \[Placeholder], 1, \[Placeholder], \[Placeholder], -1, 1, \[Placeholder], 1}, {0, 0, \[Placeholder], \[Placeholder], \[Placeholder], 0, \[Placeholder], 1, \[Placeholder], \[Placeholder], \[Placeholder], 1, -1, 1, \[Placeholder]}, {\[Placeholder], 0, 0, \[Placeholder], \[Placeholder], 0, 0, \[Placeholder], \[Placeholder], 1, 1, \[Placeholder], 1, -1, 1}, {\[Placeholder], \[Placeholder], \[Placeholder], 0, 0, 0, 0, \[Placeholder], 1, \[Placeholder], 1, 1, \[Placeholder], 1, -1}}))
varstuff=(({{1, 1, a11}, {-1, 1, 0}, {1, 1, 0}, {1, -1, 0}, {a1, 1, a12}, {1, a7, a13}, {a2, 1, a14}, {0, 0, 1}, {a3, 0, a15}, {0, 0, -1}, {a4, 0, 1}, {a5, a8, a16}, {0, a9, a17}, {0, a10, 1}, {a6, 0, a18}}))
a=1
b=11
o=vars[[a,1]]
n=vars[[a,2]]
d=vars[[a,3]]
q=vars[[b,1]]
r=vars[[b,2]]
s=vars[[b,3]]

bil[a_,b_]:=1/2((vars[[a,3]]^2+vars[[a,2]]^2-1)*(vars[[b,1]]+vars[[b,2]])/(vars[[a,1]]+vars[[a,2]])+(vars[[b,3]]^2+vars[[b,2]]^2-1)*(vars[[a,1]]+vars[[a,2]])/(vars[[b,1]]+vars[[b,2]]))-vars[[a,3]]*vars[[b,3]]-vars[[a,2]]*vars[[b,2]]==matzeros[[a,b]]

bil[1,3]&&bil[1,4]&&bil[1,7]&&bil[1,9]&&bil[1,10]&&bil[2,5]&&bil[2,8]&&bil[2,11]&&bil[3,4]&&bil[3,7]&&bil[3,9]&&bil[3,12]&&bil[4,5]&&bil[4,9]&&bil[4,10]&&bil[4,11]&&bil[4,12]&&bil[5,8]&&bil[5,11]&&bil[5,12]&&bil[7,9]&&bil[7,12]&&bil[8,11]&&bil[8,12]&&bil[9,10]&&bil[9,12]&&bil[10,11]&&bil[11,12]

vars=(({{1, 1, a11}, {1, 1, 0}, {a1, 1, a12}, {1, a7, a13}, {a2, 1, a14}, {0, 0, 1}, {a3, 0, a15}, {a4, 0, 1}, {a5, a8, a16}, {0, a9, a17}, {0, a10, 1}, {a6, 0, a18}}))

(({{1, 1, 2 (Sqrt[5])}, {1, 1, 0}, {(27/5), 1, (24/(Sqrt[5]))}, {1, (3/2), ((3 (Sqrt[5]))/2)}, {(13/5), 1, (6/(Sqrt[5]))}, {0, 0, 1}, {(8/(Sqrt[5])), 0, 7}, {(6/(Sqrt[5])), 0, 1}, {(8/(Sqrt[5])), (Sqrt[5]), 10}, {0, (Sqrt[5]), 4}, {0, ((2 (Sqrt[5]))/3), 1}, {(24/(5 (Sqrt[5]))), 0, (13/5)}}))

Solve[bil[1,3]&&bil[1,4]&&bil[1,7]&&bil[1,9]&&bil[1,10]&&bil[2,5]&&bil[2,8]&&bil[2,11]&&bil[3,4]&&bil[3,7]&&bil[3,9]&&bil[3,12]&&bil[4,5]&&bil[4,9]&&bil[4,10]&&bil[4,11]&&bil[4,12]&&bil[5,8]&&bil[5,11]&&bil[5,12]&&bil[7,9]&&bil[7,12]&&bil[8,11]&&bil[8,12]&&bil[9,10]&&bil[9,12]&&bil[10,11]&&bil[11,12]]

RootApproximant[NSolve[bil[1,3]&&bil[1,4]&&bil[1,7]&&bil[1,9]&&bil[1,10]&&bil[2,5]&&bil[2,8]&&bil[2,11]&&bil[3,4]&&bil[3,7]&&bil[3,9]&&bil[3,12]&&bil[4,5]&&bil[4,9]&&bil[4,10]&&bil[4,11]&&bil[4,12]&&bil[5,8]&&bil[5,11]&&bil[5,12]&&bil[7,9]&&bil[7,12]&&bil[8,11]&&bil[8,12]&&bil[9,10]&&bil[9,12]&&bil[10,11]&&bil[11,12]]]

{{RootApproximant[a1->5.4`],RootApproximant[a10->-1.490711984999859`],RootApproximant[a11->-4.472135954999577`],RootApproximant[a12->-10.733126291998984`],RootApproximant[a13->-3.354101966249683`],RootApproximant[a14->-2.683281572999746`],RootApproximant[a15->7.`],RootApproximant[a16->10.`],RootApproximant[a17->4.`],RootApproximant[a18->2.6`],RootApproximant[a2->2.6`],RootApproximant[a3->-3.5777087639996616`],RootApproximant[a4->-2.683281572999746`],RootApproximant[a5->-3.5777087639996616`],RootApproximant[a6->-2.146625258399797`],RootApproximant[a7->1.5`],RootApproximant[a8->-2.2360679774997885`],RootApproximant[a9->-2.2360679774997885`]},{RootApproximant[a1->5.4`],RootApproximant[a10->1.4907119849998598`],RootApproximant[a11->4.47213595499958`],RootApproximant[a12->10.73312629199899`],RootApproximant[a13->3.3541019662496847`],RootApproximant[a14->2.6832815729997477`],RootApproximant[a15->7.`],RootApproximant[a16->10.`],RootApproximant[a17->4.`],RootApproximant[a18->2.6`],RootApproximant[a2->2.6`],RootApproximant[a3->3.577708763999664`],RootApproximant[a4->2.6832815729997477`],RootApproximant[a5->3.577708763999664`],RootApproximant[a6->2.1466252583997982`],RootApproximant[a7->1.5`],RootApproximant[a8->2.23606797749979`],RootApproximant[a9->2.23606797749979`]}}

matzeros=(({{\[Placeholder], \[Placeholder], 1, 1, \[Placeholder], 0, 0, \[Placeholder], 0, 0, \[Placeholder], \[Placeholder]}, {\[Placeholder], \[Placeholder], \[Placeholder], \[Placeholder], 1, \[Placeholder], \[Placeholder], 0, \[Placeholder], \[Placeholder], 0, \[Placeholder]}, {1, \[Placeholder], \[Placeholder], 1, \[Placeholder], \[Placeholder], 0, \[Placeholder], 0, \[Placeholder], \[Placeholder], 0}, {1, \[Placeholder], 1, \[Placeholder], 1, \[Placeholder], \[Placeholder], \[Placeholder], 0, 0, 0, 0}, {\[Placeholder], 1, \[Placeholder], 1, \[Placeholder], \[Placeholder], \[Placeholder], 0, \[Placeholder], \[Placeholder], 0, 0}, {0, \[Placeholder], \[Placeholder], \[Placeholder], \[Placeholder], \[Placeholder], 1, \[Placeholder], \[Placeholder], 1, \[Placeholder], \[Placeholder]}, {0, \[Placeholder], 0, \[Placeholder], \[Placeholder], 1, \[Placeholder], \[Placeholder], 1, \[Placeholder], \[Placeholder], 1}, {\[Placeholder], 0, \[Placeholder], \[Placeholder], 0, \[Placeholder], \[Placeholder], \[Placeholder], \[Placeholder], \[Placeholder], 1, 1}, {0, \[Placeholder], 0, 0, \[Placeholder], \[Placeholder], 1, \[Placeholder], \[Placeholder], 1, \[Placeholder], 1}, {0, \[Placeholder], \[Placeholder], 0, \[Placeholder], 1, \[Placeholder], \[Placeholder], 1, \[Placeholder], 1, \[Placeholder]}, {\[Placeholder], 0, \[Placeholder], 0, 0, \[Placeholder], \[Placeholder], 1, \[Placeholder], 1, \[Placeholder], 1}, {\[Placeholder], \[Placeholder], 0, 0, 0, \[Placeholder], 1, 1, 1, \[Placeholder], 1, \[Placeholder]}}))
vars=(({{1, 1, a11}, {1, 1, 0}, {a1, 1, a12}, {1, a7, a13}, {a2, 1, a14}, {0, 0, 1}, {a3, 0, a15}, {a4, 0, 1}, {a5, a8, a16}, {0, a9, a17}, {0, a10, 1}, {a6, 0, a18}}))

MatrixForm[vars/.{a1->(27/5),a10->-((2 (Sqrt[5]))/3),a11->-2 (Sqrt[5]),a12->-(24/(Sqrt[5])),a13->-((3 (Sqrt[5]))/2),a14->-(6/(Sqrt[5])),a15->7,a16->10,a17->4,a18->(13/5),a2->(13/5),a3->-(8/(Sqrt[5])),a4->-(6/(Sqrt[5])),a5->-(8/(Sqrt[5])),a6->-(24/(5 (Sqrt[5]))),a7->(3/2),a8->-(Sqrt[5]),a9->-(Sqrt[5])}]

Clear[a11,a12,a1]

mat=(({{-1, 1, 9, 1, 1, 1, 7, 0, 0, 2 (Sqrt[5]), 4 (Sqrt[5]), 0, 0, ((4 (Sqrt[5]))/3), (4/(Sqrt[5]))}, {1, -1, 1, 1, (27/5), 1, (13/5), 0, (8/(Sqrt[5])), 0, (6/(Sqrt[5])), (8/(Sqrt[5])), 0, 0, (24/(5 (Sqrt[5])))}, {9, 1, -1, 1, 17, (7/2), 1, 2 (Sqrt[5]), 6 (Sqrt[5]), 0, 0, 7 (Sqrt[5]), 3 (Sqrt[5]), 0, (6/(Sqrt[5]))}, {1, 1, 1, -1, 1, (3/2), 1, 0, 0, 0, 0, (Sqrt[5]), (Sqrt[5]), ((2 (Sqrt[5]))/3), 0}, {1, (27/5), 17, 1, -1, 1, 9, (8/(Sqrt[5])), 0, (24/(Sqrt[5])), 6 (Sqrt[5]), 0, (8/(Sqrt[5])), ((8 (Sqrt[5]))/3), 0}, {1, 1, (7/2), (3/2), 1, -1, 1, (Sqrt[5]), (Sqrt[5]), ((3 (Sqrt[5]))/2), ((3 (Sqrt[5]))/2), 0, 0, 0, 0}, {7, (13/5), 1, 1, 9, 1, -1, (12/(Sqrt[5])), 4 (Sqrt[5]), (6/(Sqrt[5])), 0, 4 (Sqrt[5]), (12/(Sqrt[5])), 0, 0}, {0, 0, 2 (Sqrt[5]), 0, (8/(Sqrt[5])), (Sqrt[5]), (12/(Sqrt[5])), -1, 1, 1, 5, 3, 1, (7/3), (11/5)}, {0, (8/(Sqrt[5])), 6 (Sqrt[5]), 0, 0, (Sqrt[5]), 4 (Sqrt[5]), 1, -1, 7, 11, 1, 3, (17/3), 1}, {2 (Sqrt[5]), 0, 0, 0, (24/(Sqrt[5])), ((3 (Sqrt[5]))/2), (6/(Sqrt[5])), 1, 7, -1, 1, 10, 4, 1, (13/5)}, {4 (Sqrt[5]), (6/(Sqrt[5])), 0, 0, 6 (Sqrt[5]), ((3 (Sqrt[5]))/2), 0, 5, 11, 1, -1, 14, 8, 1, 1}, {0, (8/(Sqrt[5])), 7 (Sqrt[5]), (Sqrt[5]), 0, 0, 4 (Sqrt[5]), 3, 1, 10, 14, -1, 1, (13/3), 1}, {0, 0, 3 (Sqrt[5]), (Sqrt[5]), (8/(Sqrt[5])), 0, (12/(Sqrt[5])), 1, 3, 4, 8, 1, -1, 1, (11/5)}, {((4 (Sqrt[5]))/3), 0, 0, ((2 (Sqrt[5]))/3), ((8 (Sqrt[5]))/3), 0, 0, (7/3), (17/3), 1, 1, (13/3), 1, -1, 1}, {(4/(Sqrt[5])), (24/(5 (Sqrt[5]))), (6/(Sqrt[5])), 0, 0, 0, 0, (11/5), 1, (13/5), 1, 1, (11/5), 1, -1}}))

a=1
b=11
o=mat[[2,a]]
n=mat[[4,a]]
d=mat[[10,a]]
q=mat[[2,b]]
r=mat[[4,b]]
s=mat[[10,b]]

1/2((d^2+n^2-1)*(q+r)/(o+n)+(s^2+r^2-1)*(o+n)/(q+r))-d*s-n*r
mat[[a,b]]