已知函数y=x^2-(m+1)x-4(m+5)的图像与x轴交于A、B两点,A、B两点分别在x轴的正、负半轴上,且OA与OB的长之比为1:4,求m的值

令OA = k>0 ,则OB = 4k ,∴A(-k,0),B(4k,0)∵OA:OB=1:4 ,∴xA + xB = m+1 >0 ,∴m > -1而xA + xB = 3k = m + 1,∴9k^2 = (m+1)^2且有AB^2 = 25k^2 = (m+1)^2 + 16(m+5)∴25(m+1)^2 = 225k^2 = 9(m+1)^2 + 144(m+5)∴...