已知实数a,b满足a²+a-1=0,b²+b-1=0,求b/a²+a/b²
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/06 21:54:10
![已知实数a,b满足a²+a-1=0,b²+b-1=0,求b/a²+a/b²](/uploads/image/z/5910388-52-8.jpg?t=%E5%B7%B2%E7%9F%A5%E5%AE%9E%E6%95%B0a%2Cb%E6%BB%A1%E8%B6%B3a%26%23178%3B%2Ba-1%3D0%2Cb%26%23178%3B%2Bb-1%3D0%2C%E6%B1%82b%2Fa%26%23178%3B%2Ba%2Fb%26%23178%3B)
x){}KlDgض9QMZ;Q@' KmlJ҇+ЇJ$S,;ٌ}[My>{ӽ{6mqF g<ٱɎUԃxc)__b߾f=ttLv! g=ڊr[8c8cM}$8#v35
d5,'?m]w6yv >
已知实数a,b满足a²+a-1=0,b²+b-1=0,求b/a²+a/b²
已知实数a,b满足a²+a-1=0,b²+b-1=0,求b/a²+a/b²
已知实数a,b满足a²+a-1=0,b²+b-1=0,求b/a²+a/b²
显然a,b相当于方程x^2+x-1=0的两个根.
则由韦达定理得
a+b=-1
ab=-1
故b/a²+a/b²=(a^3+b^3)/(ab)^2=(a+b)((a+b)^2-2ab)/(ab)^2=……代入即可