It is given that x+1/x=3.
Find the value of x^2+1/2^2.
With steps.
F.2 Factorization
2012-01-06 4:05 am
回答 (2)
2012-01-06 4:19 am
✔ 最佳答案
您好，我是 lop，高興能解答您的問題。x + 1/x = 3
(x+1/x)^2 = 3^2
x^2 + x/x + x/x + 1/(x^2) = 9
x^2 + 1/(x^2) + 1 + 1 = 9
x^2 + 1/(x^2) = 9 - 1 - 1
x^2 + 1/(x^2) = 7
參考: Hope I Can Help You ^_^ ( From me )
2012-01-06 4:36 am
Using the formula : a^2 + 2ab + b^2 = (a+b)^2
x^2 +2(x)(1/x) +(1/x)^2 = (x + 1/x)^2
It is known that x + 1/x=3 , and 2(x)(1/x) is a constant=2(x/x)=2
x^2 +2 +1/x^2 = 3^2
x^2 + (1/x)^2 = 3^2 - 2
x^2 + 1/x^2=7
x^2 +2(x)(1/x) +(1/x)^2 = (x + 1/x)^2
It is known that x + 1/x=3 , and 2(x)(1/x) is a constant=2(x/x)=2
x^2 +2 +1/x^2 = 3^2
x^2 + (1/x)^2 = 3^2 - 2
x^2 + 1/x^2=7
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