根式 和 無理方程式

x² - 6x - √(2x² - 12x - 5) = 20

2x² - 12x - 2√(2x² - 12x - 5) = 40

(2x² - 12x - 5) - 2√(2x² - 12x - 5) = 40 - 5

設 y = √(2x² - 12x - 5) ,

y² - 2y = 40 - 5

y² - 2y - 35 = 0

(y - 7)(y + 5) = 0

y = 7 或 y = - 5 (捨去)

√(2x² - 12x - 5) = 7

2x² - 12x - 5 = 49

x² - 6x - 27 = 0

(x - 9)(x + 3) = 0

x = 9 或 x = - 3



Log2 [log3 (log4 X)] = 0

log3 (log4 X) = 1

log4 X = 3

X = 4³

X = 64

2011-03-13 13:47:15 補充：
Log2 [log3 (log4 X)] = 0

因 Log(base2) 1 = 0
所以
log3 (log4 X) = 1

因 log(base3) 3 = 1
所以
log4 X = 3

X = 4³

X = 64