在三角形ABC中a²+b²-ab=c²=2√3S△ABC 求三角形的形状?
在三角形ABC中a²+b²-ab=c²=2√3S△ABC 求三角形的形状?
数学人气：630 ℃时间：2020-02-04 04:37:30
优质解答
根据余弦定理有：a^2+b^2-2ac*cosC=c^2而现在 a^2+b^2-ac=c^2所以有 a^2+b^2-2ac*cosC=a^2+b^2-2ac即 cosC=1/2 所以 C=π/3S=1/2*ab*sinC=1/2ab*sin(π/3)=√3*ab/4而 c^2=2√3*S所以 c^2=2√3*√3*ab/4c^2=3ab/2根...
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