✔ 最佳答案
2^x +2^(2-x) = 5
2^x +(2^2)/(2^x) = 5
Multiply both sides by 2^x
(2^x)^2 +(2^2) = 5(2^x)
(2^x)^2 +(2^2) - 5(2^x) = 0
(2^x)^2 +4- 5(2^x) = 0
(2^x)^2 - 5(2^x) + 4 = 0
Factorize
Let k = 2^x
k^2 – 5k + 4 = 0
(k -2) (k-2) = 0
k = 2
2^x = 2
2^1 = 2
Therefore x = 1
Question 15:
(5^0.5 – 3^0.5) (5^0.5 – 3^o.5) (5^0.5 – 3^0.5) 5 -2((5^0.5) (3^0.5) +3
x = -------------------- = --------------------------------------- = ------------------------------
( 5^0.5 + 3^0.5) (5^0.5 + 3^0.5) (5^0.5 – 3^0.5) 5 - 3
8 -2(5^0.5)(3^0.5)
x = --------------------------- = 4 - (5^0.5) (3^0.5) = 4 - (15^0.5)
2
8x – x^2 = x(8 – x) = (4 - 15^0.5)[8 - (4 - 15^0.5 )] = (4 - 15^0.5) (4 + 15^0.5)
= 4^2 – [15^0.5]^2 = 16 – 15 = 1
8x – x^2 = 1
Comment:
You have 10 very cumbersome questions; some questions have part (a) and (b) - too many!
It is too time-consuming to type up. Yahoo platform only allows a limited space.
Let others do a few. Good luck!
2011-01-07 10:13:59 補充：
Correction:
k^2 – 5k + 4 = 0
(k -4)(k -1) = 0 [not (k-2)(k -2)]
k = 4 k =1
2^x = 4 2^x = 1
2^2 = 4 2^0 = 1
Therefore x = 2 or x = 0
Check:
2^x +2^(2-x) = 5
2^2 +2^(2-2) = 5
4 + 1 = 5
