maths&statistics

👨🏻‍🏫 學術台數學

sum chi

2009-01-08 6:21 am

1simplify (開方x + 3)^6 +(開方x -3)^6

***********only 開方x not開方x+3

2. Find the 7th term in the expansion of (2x/3+y)^11 in desending powers of x

更新1:

***********only 開方x not開方x+3 , only 開方x not開方x-3

回答 (2)

老爺子

2009-01-08 8:11 am

✔ 最佳答案

1.
[(√x) + 3]6
= (√x)6 + 6C1(√x)5(3) + 6C2(√x)4(3)2 + 6C3(√x)3(3)3 + 6C4(√x)2(3)4 + 6C5(√x)(3)5 + (3)6
= x3 + 18(√x)5 + 135x2 + 530(√x)3 + 1215x + 1458(√x) + 729

[(√x) - 3]6
= x3 - 18(√x)5 + 135x2 - 530(√x)3 + 1215x - 1458(√x) + 729

[(√x) + 3]6 + [(√x) - 3]6
= 2(x3 + 135x2 + 1215x + 729)
= 2x3 + 270x2 + 2430x + 1458

2.
The 7th term
= 11C6(2x/3)11-6y6
= 462(2x/3)5y6
= 462(32/243)x5y6
= 4928x5y6/81
=

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[匿名]

2009-01-08 7:44 am

2.The (r+1)th term
= 11C(r+1)(2x/3)^r (y)^(11-r)
when r = 6,
11C7 (2x/3)^6 (y)^5
= 330(2x/3)^6 (y)^5
= 7040/249 (x)^6 (y)^5

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