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一道数学题（英文的!）Given that P(x) is the least degree polynomial with rational coefficients such that P (√2+√3 ) =√2 ,and then P(10)=
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一道数学题（英文的!）
Given that P(x) is the least degree polynomial with rational coefficients such that P (√2+√3 ) =√2 ,
and then P(10)=
Given that P(x) is the least degree polynomial with rational coefficients such that P (√2+√3 ) =√2 ,
and then P(10)=
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答案和解析
要求次数最低
一次的含有√3,不行
二次的含有√6,不行
三次的有希望.计算如下：
令x=√2+√3
x^2=5+2√6
x^3=11√2+9√3
∴P(x)=(x^3-9x)/2
P(10)=(1000-90)/2=455
一次的含有√3,不行
二次的含有√6,不行
三次的有希望.计算如下：
令x=√2+√3
x^2=5+2√6
x^3=11√2+9√3
∴P(x)=(x^3-9x)/2
P(10)=(1000-90)/2=455
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