夏日香氣

OK~禁我姐係計到了~

lovecake

有冇方法唔洗solve個e^x...都計到??

夏日香氣

#3講左,你睇睇~

lovecake

明LA^^..多謝你呀

Simon

如何將e^x + e^(-x) = 20 這條方程
與e^x - e^(-x) 這個表達式「聯立方程」?

Simon

你應該想說
將given 的2次, 找到e^(2x) + e^(-2x) 的數值
再將part a 的表達式2次, 就會等於一個數值
然後再開方, 對不?

lovecake

e^(2x) + e^(-2x) =398
2邊 -2
變成(e^x-e^-x)^2=396..
開方就計到la

Simon

對!

夏日香氣

sorry,D命名我唔係好識表達,不如我做一次~

Simon

其實我知道你想點做了
只是字眼的問題而已

e^x + e^(-x) = 20
[ e^x + e^(-x) ] ^2 = 400
e^(2x) + 2 + e^(-2x) = 400
e^(2x) + e^(-2x) = 398

[ e^x - e^(-x) ] ^2
= e^(2x) - 2 + e^(-2x)
= 398 - 2 = 396

e^x - e^(-x) = 正負6開方11

夏日香氣

(e^x + e^-x)^2 = 20^2..........(1)
(e^x - e^-x)^2 = a^2..........(2)
(1),e^2x + 2 + e^-2x = 400..........(3)
(2),e^2x -2 + e^-2x = a^2..........(4)
(3)-(4),4 = 400 - a^2
a = +-6(11)^(1/2)

夏日香氣

多謝你的指導,我日後會清晰D架啦~

夏日香氣

RIGHT,你的表達正是我想說的野~

dicksonhang

let e^x=y 再搵返e^x既值都得

桃子

In (a), just apply the identity (a-b)^2=(a+b)^2-4ab.

Then you have to take the square root.
In this question, there is no informatiob whether x>0 or x<0 so, strictly speaking, you have to take both +ve and -ve square roots.

(If your teacher is tricky, he/she will add an requirement x<0 and many students will be trapped. )

In (b), apply the identity a^2-b^2=(a+b)(a-b).