Question

alpha and beta are the roots of x square - 2 X + 3 is equal to zero then Alpha square plus beta square is equal to​

Answer 1

Step-by-step explanation:

Let α,β are roots of x2−2x+3=0

Then α+β=2;αβ=3.

Now α+1α−1+β+1β−1=(α+1)(β+1)(α−1)(β+1)+(α+1)(β−1)

=αβ+α+β+1αβ+α−β−1+αβ−α+β−1

=αβ+α+β+12αβ−2=3+2+16−2=64=32

(α+1α−1)(β+1β−1)=(αβ+α+β+1)αβ−α−β+1

=3+2+13−2+1=

Answer 2

given à and ß are the roots of given equation —

x^2–2x+3

therfore à+ß=2 and àß=3

→à^2+ß^2=(à+ß)^2–2àß

=(2)^2–2(3)

=4–6

= -2