Help Alpha + Betaz (1 Viewer)

[SxC]

Help Alpha + Betaz (Plz Still need help no one answerd it)

the roots ov the equation x+1/x = 5

Find the value ov

i) alpha + 1/ Alpha

ii) Alpha + Beta

iii) Alpha^2 + Beta^2

can anyone help pleaz like i kinda get ii and iii but not da first one

 

[Seraph]

firstly you shoudl expand that equation

x^2 + 1 = 5
X^2 -5x + 1 = 0

so a = 1
b = - 5
c = 1

(i) no idea lol.... its just not coming to me

(ii) alpha + beta = -b/a -(-5)/1 = 5

(iii) alpha^2 + beta^2 is the same as (a+b)^2 - 2(ab) i think

so (5)^2 - 2 (ab)
now ab is essentially c/a = 1/1
(5)^2 - 2 (1)
= 23

fark this really sux doing maths on a keyboard

and yea sorry im clueless on the first one ....

 

[SxC]

its ok thx alot anyway... man i just couldnt do that one and i think its pretty eazy

 

[Seraph]

oops , you only wanted to know how to do the first one...

i really wanna know how to do it too

i)

i bet you its something really stupidly simple

and btw is this from a James Ruse paper? looks familiar

 

[SxC]

yeah it izzz any its only a question 5 like i should be getting 100% in like the first 6 or 7

 

[grimreaper]

since alpha is a root of the equation, alpha + 1/alpha = 5

 

[Doogsy]

but ur assuming β = 1/α. You can't be certain that this is true.
α+β=5 doesn't mean α+ 1/α = 5

 

[mojako]

To clear up the confusion:
x + 1/x = 5
has roots a and b

(i)
a + 1/a = 5,
since a satisfies the equation x + 1/x = 5.

(ii)
We can re-write the equation as
x² + 1 = 5x
x² - 5x + 1 = 0
because it will still have the same roots or solutions as x + 1/x = 5 (although the curves are different)

a + b = 5
(sum of roots in x² - 5x + 1 = 0)

(iii)
a² + b²
= (a+b)² - 2ab
= 25 - 2(1)
= 23

 

[JamiL]

x+1/x=5 therefore any x value on the curve make this true. since alph is a root it is part of the equation
therefor alph+1/alph=5
and alph + beta = -b/a
= 5
therefor alph + beta = alph + 1/alph
therefor 1/alph = beta
it correct ur rong doggsy

 

[monkey187]

Nah hes right.

If you work out both roots which are 5 +/- (21)^1/2 / 2 and work out root + 1/root they both turn out as 5 meaning alpha or beta + 1/alpha or beta = 5 there for alpha + 1/aplha = 5

 

[grimreaper]

well i would argue as to why im right but its explained above

 

[DAAVE]

x+1/x = 5

x^2 - 5x + 1

alpha + beta = 5/1

alpha*beta = 1

:. beta = 1/alpha

thus

alpha + 1/alpha = alpha + beta = 5

(alpha^2 + beta^2) = (alpha + beta)^2 - 2(alpha*beta)
= 5^2 - 2
= 23

 

[mojako]

thats true,
but I feel I NEED to say that
you do NOT need to do that verification thing

alpha satisfies x+1/x = 5 since it's a root
that's all you need.

and that's why its put as part(i)
if you need that verification then you'll be asked alpha+beta first before alpha+1/alpha

 

[DAAVE]

Of course it is valid to do that. I'm just suprised noone even mentioned a*b = c/a which was strange...

 

[acmilan]

Was this the 2003 JRAHS Trial? The question looks familiar

 

[smallcattle]

yes, it is the ruse 2003 trial paper