Alpha and bitter

x² – 6x + 8 = 0 then (x – 4)(x – 2) = 0 then x = 4 or 2

for other equation x = 16 or x = 4 (square of roots of above equation

so equation is (x – 16)(x – 4) = 0 or x² – 2x + 64 = 0

${ P }_{ 1 }=\alpha \beta =\frac { 8 }{ 1 } =8\\ Now\quad Find\quad an\quad equation\quad whose\quad roots\quad are\quad { \alpha }^{ 2 }\quad \& \quad { \beta }^{ 2 }\\ Sum\quad of\quad roots\\ { S }_{ 2 }={ \alpha }^{ 2 }+{ \beta }^{ 2 }={ \alpha }^{ 2 }+{ \beta }^{ 2 }+2\alpha \beta -2\alpha \beta ={ (\alpha +\beta ) }^{ 2 }-2\alpha \beta \\ ={ { ({ S }_{ 1 }) } }^{ 2 }-2{ P }_{ 1 }={ 6 }^{ 2 }-2(8)=36-16\\ \boxed { { S }_{ 2 }=20 } \\ Products\quad of\quad roots\\ { P }_{ 2 }={ \alpha }^{ 2 }{ \beta }^{ 2 }={ (\alpha \beta })^{ 2 }={ ({ P }_{ 1 }) }^{ 2 }={ 8 }^{ 2 }\\ \boxed { { P }_{ 2 }=64 } \\ To\quad find\quad Equation,\quad Use\quad this\quad formula\\ \boxed { { x }^{ 2 }-Sx+p=0 } \quad we\quad have\\ =>\quad \quad \qquad \qquad \boxed { { x }^{ 2 }-20x+64=0 } \quad ans...........\\$