资质 |代数 |问题 1
如果 x 3 + y 3 = 9 且 x + y = 3,则 x 4 +y 4的值是,
(一) 21
(乙) 0
(三) 17
(四) 25答案: (C)
解释:
x3+y3 = (x + y) × (x2 − xy + y2)
Putting given values of x3+y3 and (x + y)
9 = 3 × ((x+y)2 − 3xy)
= 3 × (9 − 3xy)
= 27 − 9xy
9xy = 18
xy = 2
x4 + y4 = (x2 + y2)2 - 2x2y2
= (x2 + y2)2 - 2*4
[Putting value of xy]
= ((x + y)2 - 2xy)2 - 2*4
[Putting values of (x+y) and xy]
= (9 - 4)2 - 2*4
= 17
这个问题的测验