Question

If p is not equal to q and p^2=5p-3 and q^2=5q-3 the equation having roots as p/q and q/p is what
a) x^2-19x+3=0
b) 3x^2-19x-3=0
c) 3x^2-19x+3=0
d) 3x^2+19x+3=0​

Answer 1

Answer:

p = (5±√13)/2

q = (5±√13)/2

If p≠q then one is (5+√13)/2 and the other is (5-√13)/2

(5+√13)/(5-√13) = (19+5√13)/6

(5-√13)/(5+√13) = (19-5√13)/6

So, the equation is

(x-((19+5√13)/6))(x-((19-5√13)/6)) = 0

(6x-19-5√13)(6x-19+5√13) = 0

(6x-19)^2 - 325 = 0

36x^2 - 228x + 36 = 0

3x^2 - 19x + 3 = 0