急 ~~ 解方程

1) 5 - 2/y = 2y

y ( 5 - 2 / y ) = 2y ^ 2

5y - 2 = 2y ^ 2

2y ^ 2 - 5y + 2 = 0

by Quadratic formula ,


圖片參考：http://upload.wikimedia.org/math/3/e/a/3ea647783b5121989cd87ca3bb558916.png


y = [ 5 + or - √ ( -5 ^ 2 - 4 ( 2 ) ( 2 ) ) ] / [ 2 ( 2 ) ]

y = 23 / 4 or 17 / 4

2) n/2 + 10 = 2/5n

10n ( n / 2 + 10 ) = 10n ( 2 / 5n )

5n ^ 2 + 20n = 4

5n ^ 2 + 20n - 4 = 0

by Quadratic formula ,


圖片參考：http://upload.wikimedia.org/math/3/e/a/3ea647783b5121989cd87ca3bb558916.png


n = - 20 + or - √ ( 20 ^ 2 - 4 ( 5 ) ( 4 ) ) / [ 2 ( 5 ) ]

n = - 2 + or - ( √ 320 ) / 10

n ~ 3.78885 or - 0.21114

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2) n/2 + 10 = 2/5n
10(n/2 + 10) = (2/5)n ?
5n + 100 = 4n
n = -100

or n/2 + 10 = 2/(5n) ?
10n(n/2 + 10) = 10n[2/(5n)]
5n^2 + 100n = 4
5n^2 + 100n - 4 = 0
By quadratic formula,
n = {-100 ± √[100^2 - 4(50)(-4)]} / 2(5)
= {-100 ± √10800} / 10
= (-100 ± 60√3) / 10
= -10 ± 6√3