18 Jun '05 07:17

Let a and b be the roots of the quadratic equation x^2 + x - 1 = 0.

Find the value of a^6 + b^6.

Find the value of a^6 + b^6.

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slatington, pa, usa23 Jun '05 21:51

I did it on my calculator, a casio fx-115ms, and without*Originally posted by ilywrin***I guess you mean positive "even" exponent?**

parenthesis it comes out as a minus. But like you said,

any minus number raised to an even exponent has to be +.

It turns out you need to put the number and minus sign inside

the parenthesis, (-1.6)^6=+17......

going -1.6^6 on the casio, no parentheisis, gives -17......- Joined
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slatington, pa, usa24 Jun '05 15:37

here is another question: can X^2+X-1 be factorized?*Originally posted by phgao***Let a and b be the roots of the quadratic equation x^2 + x - 1 = 0.**

Find the value of a^6 + b^6.

llike X^2-1 is (X-1)*(X+1)

x^2-2X+1 is (X-1)^2 and X^2+2X+1 is (X+1)^2

That pretty much kills all the x and 1 combinations so is there a

regular factoriztion for this formula? Already know the roots.- Joined
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slatington, pa, usa25 Jun '05 01:40

well, learn something new every day. so if root 1 is called R1 and*Originally posted by ilywrin***Well IIRC any polynomial may be written as:**

a(x - z1) (x-z2)...(x- zn), where a is the coefficient before the highest power of x, and z1,..,zn are all the roots.

root 2 is called R2 then for x^2-X-1 it goes (X-R1)*(X-R2) right?- Joined
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