Quadratic Polynomial question... i need help again plz (1 Viewer)

[physician]

I hope u mathematicians are awake...

ok well here it goes...

a and b are the roots of the equation x² - (m² + n²)x + mn = 0. If 3(a + b) = 10ab, show that m = n/3 or m=3n...

any help would be greatly appreciated

 

[physician]

sorry dudes but i need to bump the thread .. i have an exam tmrw.. i should've asked earlier... but i thought i'd figure out how to do it....

once again i apologise for any inconvenience...

 

[physician]

.... anyonnnneeeee.... plzzzz.... *begins to sob (internally)*

 

[FinalFantasy]

a and b are the roots of the equation x^2 - (m^2 + n^2)x + mn = 0. If 3(a + b) = 10ab, show that m = n/3 or m=3n...

x²-(m²+n²)x+mn=0
3(a+b)=10ab

a+b=(m²+n²)
ab=mn
10ab=10mn
.: 10mn=3(a+b)
10mn=3(m²+n²)
3m²-10mn+3n²=0
sub in m=n\3
3(n\3)²-10n(n\3)+3n²=n²\3-10n²\3+3n²=0
.: m=n\3

sub m=3n den it should hold
or if u dun like the idea of subbing things in.. just use 3m²-10mn+3n²=0 and factorise it.. i can't be bothered to do dat lol

 

[haboozin]

a + b = m^2 + n^2 (by definition)
ab = mn (as above)



3m^2 + 3n^2 = 10mn


<i>m = n/3 or m=3n</i>

3m^2 + 3n^2 - 10mn = 0

put in n/3 for m

n^2/3 + 3n^2 - 10n^2/3 = 0 as required

m = 3n
= 0 as required

therefore m=n/3 or 3n

you can also do this by factorizing or using the quadratic formula

 

[physician]

whatt... lol never knew we could sub them in....

oh yeh that's how ur supposed to show... lol

never even thought of doing that....

thank u soo soooo much guys.... thanku thank u thank u!!!

 

[FinalFantasy]

a and b are the roots of the equation x2 - (m2 + n2)x + mn = 0. If 3(a + b) = 10ab, show that m = n/3 or m=3n...
if u don't sub in...
3m²-10mn+3n²=0

u can look at what it ask u to show and make the equation out of dat:
(m-n\3)(m-3n)=0
m²-3mn-mn\3+n²=0
times 3 to the whole thing
3m²-10mn+3n²=0