If alpha and beta are the roots of x2-2x+3 then find the value of alpha/beta2 + beta/alpha2
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Step-by-step explanation:3x 2 −2x+1=0
Let α,β are roots of x 2 −2x+3=0
Then α+β=2;αβ=3.
Now α+1 α−1 + β+1 β−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−2
= 3+2+1 6−2
= 6 4
= 3 2
( α+1 α−1 )( β+1 β−1 )= (αβ+α+β+1) αβ−α−β+1
= 3+2+1 3−2+1
= 6 2
= 3 1
Hence, equation is x 2 −( 32 )x+( 3 1 )=0⇒3x 2 −2x+1=0.
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