a,b,c是三角形ABC三边,满足a²+b²=10a+8b-41,c为最长边且为整数,c为那几个数?
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![a,b,c是三角形ABC三边,满足a²+b²=10a+8b-41,c为最长边且为整数,c为那几个数?](/uploads/image/z/2590787-11-7.jpg?t=a%2Cb%2Cc%E6%98%AF%E4%B8%89%E8%A7%92%E5%BD%A2ABC%E4%B8%89%E8%BE%B9%2C%E6%BB%A1%E8%B6%B3a%26%23178%3B%EF%BC%8Bb%26%23178%3B%EF%BC%9D10a%2B8b-41%2Cc%E4%B8%BA%E6%9C%80%E9%95%BF%E8%BE%B9%E4%B8%94%E4%B8%BA%E6%95%B4%E6%95%B0%2Cc%E4%B8%BA%E9%82%A3%E5%87%A0%E4%B8%AA%E6%95%B0%3F)
a,b,c是三角形ABC三边,满足a²+b²=10a+8b-41,c为最长边且为整数,c为那几个数?
a,b,c是三角形ABC三边,满足a²+b²=10a+8b-41,c为最长边且为整数,c为那几个数?
a,b,c是三角形ABC三边,满足a²+b²=10a+8b-41,c为最长边且为整数,c为那几个数?
a²-10a+25+b²-8b+16=0
(a-5)²+(b-4)²=0
则:a-5=0,b-4=0
∴a=5,b=4
则:a-b
a²+b²=10a+8b-41
a²-10a+b²-8b+41=0
(a-5)²+(b-4)²=0
a=5,b=4
a-b
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a²+b²=10a+8b-41
a²+b²-10a-8b+41=0
(a²-10a+25)+(b²-8b+16)=0
(a-5)²+(b-4)²=0
{a-5=0
b-4=0
∴a=5,b=4
∴5-4<c<5+4
即1<c<9
∵c为最长边且为整数
∴c是5,6,7,8
我靠,全是学霸,都还给数学老师了。。。
楼下的学霸、你们够了