在三角形ABC中，若A+C=2B,三角形面积为根号3，且log4sinA+log4sinC=-1则它的三条边长分别为a=___b=___ c=___
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A+C=2B, == B=60, log4sinA+log4sinC=-1 == sinAsinC = 1/4面积 = 根号3 = a*b*sinC/2 ...(1)面积 = 根号3 = b*c*sinA/2 ...(2)面积 = 根号3 = c*a*sinB/2 = c*a*[(根号3)/2]/2...(3)(3): == c*a = 4 ...(4)(1)*(2): 12 = a*b^2*c*(sinAsinC) = a*b^2*c*(1/4) = b^2 == b=2*根号3b^2 = a^2 + c^2 - 2ac*cosB === a^2 + c^2 = 16 ...(5)(4)(5): a = 根号6 + 根号2, c = 根号6 - 根号2因此：三条边长分别为：a = 根号6 + 根号2；b=2*根号3；c = 根号6 - 根号2。