1.已知△ABC的三条边长分别为a,b,c,且满足a=7+b,ab=120,c=17,△ABC是直角三角形吗?请证明.2.已知△ABC的三条边长分别为a,b,c,且满足|a-12|+b²+256+根号（10-1/2c）=32b,△ABC是直角三角形吗?请证明.

Question

1.已知△ABC的三条边长分别为a,b,c,且满足a=7+b,ab=120,c=17,△ABC是直角三角形吗?请证明.
2.已知△ABC的三条边长分别为a,b,c,且满足|a-12|+b²+256+根号（10-1/2c）=32b,△ABC是直角三角形吗?请证明.

Answer 1

1、a=7+b => (a-b)^2=49 => a^2+b^2=49+2ab=49+240=289=17^2 = c^2 所以是直角三形.
2、|a-12|+b²+256+根号（10-1/2c）=32b => |a-12|+(b-16)^2 = -根号(10-1/2c)
所以 a=12,b=16,c=20 满足a^2+b^2= c^2 所以是直角三形