Question

if alpha and beta are the roots of x^2-x+2=0 find the equation whose roots are 1/alpha^2.beta and 1/alpha.beta^2​

Answer 1

Answer:

Check the solution below.

Step-by-step explanation:

Since, αandβ are the roots of the equation

x2−2x−1=0, then

Sum of roots , α+β=2 and

product of the roots αβ=−1

Since, (α+β)=α2+β2+2αβ

⇒4=α2+β2−2

⇒α2+β2=6

Now, α2β−2+α−2β2=α2β2+β2α2=α4+β4(αβ)2

⇒(α2+β2)2=62

⇒α4+β4+2α2β2=36 (∵αβ=−1)

⇒α4+β4=34  ...(i)

⇒α4+β4(αβ)2=34(−1)2=34

[ Putting value of α4+β4=34 from Equation (i)]