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if a and b are the roots of the quadratic equation x^2+x+1 then give the equation whos roots are a^14 and b^26
a=-b
a2=b2
a14=(a2)7=m7
b26=(b2)13=(a2)13=m13
(x-m7)(x-m13)=0
x2-(m6+1)m7x+m20
x2-(a12+1)a14x+a40
a=w, b=w^2 where w is a complex cube root of unity
a^14 = w^14 = (w^12).(w^2) = w^2
b^26 = w^52 = (w^51)(w)=w
therefore, the required equation is
x^2 - (w+w^2)x + (w^3)=0
=>x^2 + x + 1=0, that is, the given equation....
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