已知x=1/2log2.5(2為底5是對數) 則4的x次方加上4的-x次方等於？ 若x=根號3加一 求log2(x四次方+4x三次方-x平方-10x+22)等於？ 求這兩題答案和詳解 謝謝?
回答 (1)
2016-08-04 11:04 pm
4ˣ + 4⁻ˣ
= 4^((log₂5)/2) + 4^(-(log₂5)/2)
= 2^log₂5 + 2^-log₂5
= 5 + 1/5
= 5.2
x = √3 - 1
(x + 1)² = 3 ⇒ x² = 2 - 2x
(x + 1)⁴= 9
x⁴+ 4x³ + 6x² + 4x - 8 = 0
x⁴+ 4x³ - x² - 10x + 22 = - 7x² - 14x + 30 = - 7(2 - 2x) - 14x + 30 = 16
∴ log₂(x⁴+ 4x³ - x² - 10x + 22) = log₂16 = 4
= 4^((log₂5)/2) + 4^(-(log₂5)/2)
= 2^log₂5 + 2^-log₂5
= 5 + 1/5
= 5.2
x = √3 - 1
(x + 1)² = 3 ⇒ x² = 2 - 2x
(x + 1)⁴= 9
x⁴+ 4x³ + 6x² + 4x - 8 = 0
x⁴+ 4x³ - x² - 10x + 22 = - 7x² - 14x + 30 = - 7(2 - 2x) - 14x + 30 = 16
∴ log₂(x⁴+ 4x³ - x² - 10x + 22) = log₂16 = 4
收錄日期: 2021-04-30 21:45:14
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