a[y-b/(2a)]^2+b[y-b/(2a)]+c=0怎么化简成a[y-b/(2a)]^2=ay^2-by+b^2/4a
问题描述:
a[y-b/(2a)]^2+b[y-b/(2a)]+c=0怎么化简成a[y-b/(2a)]^2=ay^2-by+b^2/4a
答
用乘法公式(a-b)^2=a^2-2ab+b^2展开即可
a[y-b/(2a)]^2=a[y^2-2yb/2a+b^2/4a^2]=ay^2-by+b^2/4ax=y-b/(2a)代入 ax^2+bx+c=0 a[y-b/(2a)]^2+b[y-b/(2a)]+c=0求出 y^2 = (b^2- 4ac )/(4a^2)把y^2 = (b^2- 4ac )/(4a^2) 代入 x=y-b/(2a)再怎么化简求出x?若a>0,则y=√(b^2- 4ac )/(2a), 代入 x=y-b/(2a)得 x=√(b^2- 4ac )/(2a)-b/(2a)=[√(b^2- 4ac ) -b]/(2a)若a