Question

if alpha and beta are the roots of x square is equal to X + 1 then value of Alpha square upon beta minus beta square upon Alpha is​<br />​

Answer 1

Answer:

-2√5

Step-by-step explanation:

x² = x + 1

x² - x - 1 = 0

//if quadratic equation is of form ax²+bx+c =0, then sum of roots = -b/a; product of roots = c/a.

Let α and β be the roots of the equation x² - x - 1

α + β = -(-1)/1 = 1

αβ = -1/1 = -1

(α - β)² = (α + β)² - 4αβ = 1 + 4 = 5 => α - β = √5

(α + β)² = 1

α² + β² + 2αβ = 1

α² + β² = 3

α²/β - β²/α =  α³ - β³/αβ = (α - β)(α² + β²+αβ) / αβ

  = √5(3-1)/-1 = -2√5