Lol I need to stop doing the problems from the thumbnail. I got stuck cause I was like what are we solving? Then again, I should have known that there's 1 equation with 2 unknowns, so it's not like I could have solved for either
I'm going to call golden ratio = y in this equation. putting the -1 to left side and using the quadratic formula we get x = -y or y^(-1) Question wants you to answer (x^8 +x +34)/x Plug the answers we got in the first equation then you can find the exact value using binomial expression.
if xx = 1-x then x = (-1 +- sqrt5)/2 let k be such that: kx = x^8 + x + 34 if f[n] is the nth Fibonacci number, then it's easy to show that: (f[n] - f[n+1]x) (1 - x) = f[n+2] - f[n+3]x and since x^8 = (1-1x)^4 and 1 = f[0] = f[1] we get x^8 = 13 - 21x and so the problem becomes k = 47/x - 20 Plugging in the known values of x we get: k = (7 +- 47sqrt[5])/2 which are approx: -49.047597471245057865615581215181 or 56.047597471245057865615581215185
Lol I need to stop doing the problems from the thumbnail. I got stuck cause I was like what are we solving? Then again, I should have known that there's 1 equation with 2 unknowns, so it's not like I could have solved for either
@ SyberMath Shorts -- You should put the arguments inside of grouping symbols: ln[(a + b)/3] = [ln(a) + ln(b)]/2.
ab/(a+b)=e , ab/(a+b)=e^2/e , ab=e^2 , a+b=e , b=(e+/-e*i*V3)/2 , a=(3e+/-e*i*V3)/2 ,
Solve my problem if you are really capable of I guess
IT IS AS FOLLOWS:
if x^2+x=1
then x^7+34/x+1=?
I'm going to call golden ratio = y in this equation.
putting the -1 to left side and using the quadratic formula we get x = -y or y^(-1)
Question wants you to answer (x^8 +x +34)/x
Plug the answers we got in the first equation then you can find the exact value using binomial expression.
Or you can use fibonacci series to find the answer If you know that trick as well.
if xx = 1-x
then x = (-1 +- sqrt5)/2
let k be such that:
kx = x^8 + x + 34
if f[n] is the nth Fibonacci number, then it's easy to show that:
(f[n] - f[n+1]x) (1 - x) = f[n+2] - f[n+3]x
and since x^8 = (1-1x)^4
and 1 = f[0] = f[1]
we get x^8 = 13 - 21x
and so the problem becomes
k = 47/x - 20
Plugging in the known values of x we get:
k = (7 +- 47sqrt[5])/2
which are approx:
-49.047597471245057865615581215181
or
56.047597471245057865615581215185
This is not hard at all