Question

if the roots of x²+2x-3 =0 are alpha and beta then the equation of roots alpha², beta²​

Answer 1

Let α,β are roots of x 2−2x+3=0

Then α+β=2;αβ=3.

Now

α+1

α−1 + β+1β−1 = (α+1)(β+1)(α−1)(β+1)+(α+1)(β−1) = αβ+α+β+1 αβ+α−β−1+αβ−α+β−1 = αβ+α+β+1 2αβ−3 = 3+2+1 6−2 = 6 = 32( α+1 α-2 )( β+1 β−1 )= (αβ+α+β+1) αβ−α−β+1 = 3+2+1 3−2+1 = 62 = 31

Hence, equation is x −( 32 )x+( 31 )=0⇒3 x 2 −2x+1=0.