Thread: determining the value of K

1. determining the value of K

the Given K^2-3K+5 = 0
determine the value of K^4-6K^3+9K^2-7.

if i were to solve this ... i will use the quadratic formula to solve the K. and if the value of K is solve then i will plug in to the expression K^4-6K^3+9K^2-7. Am i doing it right? if not please Guide me on this ...

Thank you and God Bless

2. Re: determining the value of K

Yes that's correct, but there's a much faster way that doesn't involve using a calculator. Square the first equation:

$\displaystyle (k^2 - 3k + 5)^2 = 0^2$

$\displaystyle k^4 - 6k^3 + 19k^2 - 30k + 25 = 0$

$\displaystyle \Rightarrow (k^4 - 6k^3 + 9k^2 - 7) + 10k^2 - 30k + 32 = 0$

$\displaystyle \Rightarrow (k^4 - 6k^3 + 9k^2 - 7) + 10(k^2 - 3k + 5) - 28 = 0$

And since $\displaystyle k^2 - 3k + 5 = 0$, we have

$\displaystyle (k^4 - 6k^3 + 9k^2 - 7) - 28 = 0$. The desired expression is equal to 28.

3. Re: determining the value of K

from the bottom of my heart... a million thanks to you sir..