Question

If a + b, but a2 = 5a - 3 and b2 = 5b-3, find a quadratic equation
whose roots are a/b and b/a
​

Answer 1

Answer:

Clearly, a & b are the roots of x^2 -5x +3 = 0.

a + b = 5

ab = 3

Sum of roots of the reqd equation,

S' = a/b +b/a = a^2 + b^2 / ab. = 19/3

Product of roots = 1

So the required equation is

x^2 -19/3 x + 1 = 0

Or 3x^2 -19 x + 3 = 0