Question

α ≠ β, but α² = 5α - 3,β² = 5β - 3, then find the equation whose roots are α/β  and β/α.

Answer 1

α and β are roots of x² - 5x + 3 = 0. Therefore, α + β = 5, αβ = 3. So S = 5(5) - 6/3 = 19/3

Therefore,

x² - 19/3 x + 1

⇒ 3x² - 19x + 3 = 0