12sin^2 pi*x/102 + 8 cos pi*x/102=13

Question

12sin^2 pi*x/102 + 8 cos pi*x/102=13

Answer 1

12-12cos²πx/102+8cosπx/102=13
a=cosπx/102
12a²-8a+1=0
D=64-48=16
a1=(8-4)/24=1/6⇒cosπx/102=1/6
πx/102=+-arccos1/6+2πn,n∈z
x=+102/π*arccos1/6+204n,n∈z
a2=(8+4)/24=1/2⇒cosπx/102=1/2
πx/102=+-π/3+2πk,k∈x
x=+-34+204k,k∈z