請問以下呢題數點攸呀?
It is given that x+1/x=3
(a)Find the valve of x^2+1/x^2 .
(b)Using the result of (a), find the value of x^3+1/x^3 .
f.3數學點做?
2011-08-21 9:50 pm
回答 (3)
2011-08-22 12:20 am
✔ 最佳答案
(a) x+1/x=3 <---[Square both sides](x+1/x)²=9
x²+2x(1/x)+1/(x²)=9
x²+2+1/x²=9
x²+1/x²=7
(b) x²+1/x²=7 <---[Bothsides time (x+1/x)]
(x²+1/x²)(x+1/x)=3(x+1/x)
x³+x/x²+x²/x+1/x³=3*7
x³+1/x³+(x+1/x)=21
x³+1/x³+3=21
x³+1/x³=18
參考: Hope I can help you! ^_^ (From me)
2011-08-22 5:22 am
x^3+1/x^3
(x+(1/x))+(x^2+1+(1/x^2))
3(8)
=24
(x+(1/x))+(x^2+1+(1/x^2))
3(8)
=24
2011-08-21 10:18 pm
x + 1/x = 3
(a) x^2 + 1/x^2
= (x + 1/x)^2 - 2
= 9 - 2
= 7
(b) x^3 + 1/x^3
= (x + 1/x)^3 - 3(x)(1/x)(x + 1/x)
= 27 - 3
= 24
(a) x^2 + 1/x^2
= (x + 1/x)^2 - 2
= 9 - 2
= 7
(b) x^3 + 1/x^3
= (x + 1/x)^3 - 3(x)(1/x)(x + 1/x)
= 27 - 3
= 24
收錄日期: 2021-04-13 18:10:56
原文連結 [永久失效]:
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