Question

If x²-3x+1=0 then x^10-123x^5+1=?


I can't get the ans pls help. ​

Answer 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

Check out this solution.

Answer 2

Answer:

I don't know mbdjjdksbd