25x2+x+1=0 By Viet Theorem
α2+β2=−251
α2β2=251 Then
α21+β21=α2β2α2+β2
=251−251=−1
αβ=−51 or αβ=51
αβ=−51
α1(β1)=−5
(α1+β1)2=α21+β21+αβ2
=−1+2(−5)=−11
α1+β1=−i11 or α1+β1=i11 The quadratic equation is
y2+i11y−5=0 Or
y2−i11y−5=0
αβ=51
α1(β1)=5
(α1+β1)2=α21+β21+αβ2
=−1+2(5)=9
α1+β1=−3 or α1+β1=3
The quadratic equation is
y2+3y+5=0 Or
y2−3y+5=0
y2+i11y−5=0
y2−i11y−5=0
y2+3y+5=0
y2−3y+5=0
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