a difficult math questionx^2-3x+1=0,x^4+1/x^4=?,why?
问题描述：
a difficult math question
x^2-3x+1=0,x^4+1/x^4=?,why?
答
∵x^2-3x+1=0
∴ x+1/x=3
∴ x^2+1/x^2=(x+1/x)^2-2=7
∴ x^4+1/x^4=(x^2+1/x^2)^2-2=47
答
x^2+1 = 3x
so x+1/x = 3
(x+1/x)^2 = 9
then x^2+1/x^2 = 7
(x^2+1/x^2)^2 = 49
x^4+1/x^4=47
答
x^2-3x+1=0两边同时除以x得
x + 1/x =3
两边同时平方得
x^2 + 1/x^2 =7
两边再次平方得
x^4 + 1/x^4 =47
答
∵x^2-3x+1=0
两边同除以x得到
x+(1/x)=3
平方得到
x^2+(1/x^2)=7
再平方得到
x^4+(1/x^4)=47
答
From the factor,we can get that x+1/x=3
so (x+1/x)^2=x^2+1/x^2+2=9 x^2+1/x^2=7
so (x^2+1/x^2)^2=x^4+1/x^4+2=49 x^4+1/x^4=47