If
x² – 3x + 1 = 0
then
x^10-123x^5+1=?
plss anwer
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1
Answer:
There is another way to solve it.
x2-3x+1=0 <---(1). [x2+1=3x]
x5+1/x5=?
(x+1/x)=(x2+1)/x=|due to (1)|=3x/x=3. <---(2)
(x+1/x)5=x5+5x3+10x+10/x+5/x3+1/x5=
=x5+1/x5+10(x+1/x)+5(x3+1/x3)
x5+1/x5=(x+1/x)5-10(x+1/x)-5(x3+1/x3)=
=(x+1/x)5-10(x+1/x)-5(x+1/x)(x2+1/x2-2) <---- (3)
From (2) we have
(x+1/x)=3
x2+2+1/x2=9
x2+1/x2=7
x5+1/x5=(x+1/x)5-10(x+1/x)-5(x+1/x)(x2+1/x2-2)
= 35-10*3-5*3*5=3(81-10-25)=3*46=138
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