已知x＋y＝3,x²＋y²－xy＝4,求x⁴＋y⁴＋x³y＋xy³_数学解答

已知x＋y＝3,x²＋y²－xy＝4,求x⁴＋y⁴＋x³y＋xy³的值

人气：383 ℃　时间：2020-02-05 03:21:37

解答

x⁴＋y⁴＋x³y＋xy³
=(x⁴+x³y)+(xy³+y⁴)
=x³(x+y)+y³(x+y)
=(x+y)(x³+y³)
=(x+y)(x+y)(x²+y²-xy)
=(x+y)²(x²+y²-xy)
=3²×4
=36