another sum and product of the roots question (1 Viewer)

[miracu]

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.

I don't know if I'm on the right track but I wrote 3(m^2 + n^2) = 10mn.
Not sure how to solve from there.

 

[DatAtarLyfe]

You're pretty much there:
3m^2 -10mn + 3n^2 = 0
3m^2 -9mn -mn + 3n^2 = 0
3m (m - 3n) - n (m - 3n) = 0
(3m - n)(m - 3n) = 0
Therefore, m = n/3 or m = 3n, as required.

 

[Esse]

Keep going bro. 3m²-10mn+3n²
(3m - n)(M - 3n)
m=n/3 and m=3n

 

[Esse]

Omg the 1 min early reply xd