tanα=3的x次方,tanβ=3的-x次方,α-β=π/6,x=
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tanα=3的x次方,tanβ=3的-x次方,α-β=π/6,x=
tanα=3的x次方,tanβ=3的-x次方,α-β=π/6,x=
tanα=3的x次方,tanβ=3的-x次方,α-β=π/6,x=
tanα=3^x,tanβ=3^(-x),α-β=π/6,x=
∵tanα=3^x,tanβ=3^(-x),
∴tanα*tanβ=1
α-β=π/6
∴tanπ/6=tan(α-β)=(tanα-tanβ)/(1+tanα*tanβ)
=[3^x-3^(-x)]/(1+1)=√3/3
即 3^x-3^(-x)=2√3/3 (*)
设 3^x=t t>0 则(*)化为 t-1/t=2√3/3
也就是t^2-2√3/3t-1=0
因式分解的(t-√3)(t+√3/3)=0
t>0 t+√3/3>0
∴t-√3=0
t=√3
3^x=3^(1/2)
x=1/2