△ABC中,a^2+b^2-ab=c^2=2根号3S△ABC,求三角形形状 网上答案我看不懂S=absinC/2=√3ab/4c^2=2√3S=3ab/2所以:a^2+b^2-ab=c^2=3ab/2解得:a=b/2或者a=2b结合c^2=3ab/2得a=b/2时c=√3b/2或者a=2b时c=√3b.当a=b/2时c=√3b/2
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![△ABC中,a^2+b^2-ab=c^2=2根号3S△ABC,求三角形形状 网上答案我看不懂S=absinC/2=√3ab/4c^2=2√3S=3ab/2所以:a^2+b^2-ab=c^2=3ab/2解得:a=b/2或者a=2b结合c^2=3ab/2得a=b/2时c=√3b/2或者a=2b时c=√3b.当a=b/2时c=√3b/2](/uploads/image/z/987359-23-9.jpg?t=%E2%96%B3ABC%E4%B8%AD%2Ca%5E2%2Bb%5E2-ab%3Dc%5E2%3D2%E6%A0%B9%E5%8F%B73S%E2%96%B3ABC%2C%E6%B1%82%E4%B8%89%E8%A7%92%E5%BD%A2%E5%BD%A2%E7%8A%B6+%E7%BD%91%E4%B8%8A%E7%AD%94%E6%A1%88%E6%88%91%E7%9C%8B%E4%B8%8D%E6%87%82S%3DabsinC%2F2%3D%E2%88%9A3ab%2F4c%5E2%3D2%E2%88%9A3S%3D3ab%2F2%E6%89%80%E4%BB%A5%EF%BC%9Aa%5E2%2Bb%5E2-ab%3Dc%5E2%3D3ab%2F2%E8%A7%A3%E5%BE%97%EF%BC%9Aa%3Db%2F2%E6%88%96%E8%80%85a%3D2b%E7%BB%93%E5%90%88c%5E2%3D3ab%2F2%E5%BE%97a%3Db%2F2%E6%97%B6c%3D%E2%88%9A3b%2F2%E6%88%96%E8%80%85a%3D2b%E6%97%B6c%3D%E2%88%9A3b.%E5%BD%93a%3Db%2F2%E6%97%B6c%3D%E2%88%9A3b%2F2)
△ABC中,a^2+b^2-ab=c^2=2根号3S△ABC,求三角形形状 网上答案我看不懂S=absinC/2=√3ab/4c^2=2√3S=3ab/2所以:a^2+b^2-ab=c^2=3ab/2解得:a=b/2或者a=2b结合c^2=3ab/2得a=b/2时c=√3b/2或者a=2b时c=√3b.当a=b/2时c=√3b/2
△ABC中,a^2+b^2-ab=c^2=2根号3S△ABC,求三角形形状 网上答案我看不懂
S=absinC/2=√3ab/4
c^2=2√3S=3ab/2
所以:a^2+b^2-ab=c^2=3ab/2
解得:a=b/2或者a=2b
结合c^2=3ab/2得a=b/2时c=√3b/2或者a=2b时c=√3b.
当a=b/2时c=√3b/2时:a^2+c^2=b^2
当a=2b时c=√3b时,b^2+c^2=a^2
这个解得是怎么解出来的?
△ABC中,a^2+b^2-ab=c^2=2根号3S△ABC,求三角形形状 网上答案我看不懂S=absinC/2=√3ab/4c^2=2√3S=3ab/2所以:a^2+b^2-ab=c^2=3ab/2解得:a=b/2或者a=2b结合c^2=3ab/2得a=b/2时c=√3b/2或者a=2b时c=√3b.当a=b/2时c=√3b/2
c^2=a^2+b^2-ab
公式c^2=a^2+b^2-2abCosc
对比一下发现ab=2abCosc,所以Cosc=1/2,Sinc=√3/2
S=absinC/2,sinC换成√3/2,所以S=√3ab/4
c^2=2√3S,S=√3ab/4所以c^2=3ab/2=而c^2=a^2+b^2-ab,所以a^2+b^2-ab=3ab/2
得a^2+b^2=5ab/2
所以2a^2+2b^2=5ab,然后随机选择a^2或b^2
例如a^2,等式各项除以a^2
得2+2b^2/a^2=5b/a
设b/a=X,则等式为2+2X^2=5X
就是一个一元二次方程,解得X=1/2
所以a=2b.
如果除以b^2,则得a=b/2
所以当a=b/2时c=√3b/2时:a^2+c^2=b^2当a=2b时c=√3b时,b^2+c^2=a^2