△ABC的三边A,B,C满足²-10A+C²-26C+194+√(2/3B-8)=0试求A,B,C的值,并判断△ABC的形状

△ABC的三边A,B,C满足²-10A+C²-26C+194+√(2/3B-8)=0试求A,B,C的值,并判断△ABC的形状
△ABC的三边A,B,C满足²-10A+C²-26C+194+√(2/3B-8)=0试求A,B,C的值,并判断△ABC的形状

△ABC的三边A,B,C满足²-10A+C²-26C+194+√(2/3B-8)=0试求A,B,C的值,并判断△ABC的形状
A²-10A+C²-26C+194+√(2/3B-8)=0
A²-10A+25+C²-26C+169+√(2/3B-8)=0
(A-5)²+(C-13)²++√(2/3B-8)=0
所以A=5,C=13 ,B=12
因为13²=12²+5²
所以△ABC是以c边为斜边的直角三角形