Question

鯊西米

想請問這一題怎麼解 謝謝😊

3. 已知x為實數且滿足x²-4x+1=0,則x+
141x√3.
= 2+√3
+3=
X = 8+3.3
Ans:52
>> 高師附中

Answer 1

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我就是我

x²-4x+1=0
x-4+1/x=0
x+1/x=4

x²-x·1/x+1/x²=(x+1/x)²-3·x·1/x=4²-3=13

x³+1/x³=(x+1/x)(x²-x·1/x+1/x²)=4·13=52

Answer 2

珏

(a+b)³=a³+3a²b+3ab²+b³