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Question Number 204658 by hardmath last updated on 24/Feb/24

If a = (9)^(1/3) − (3)^(1/3) + 1 Find (((4 − a)/a))^6 = ?

Ifa=93−33+1Find(4−aa)6=?

Answered by Rasheed.Sindhi last updated on 24/Feb/24

a = (9)^(1/3) − (3)^(1/3) + 1; (((4 − a)/a))^6 = ? let (3)^(1/3) =t⇒t^3 =3 a=t^2 −t+1 (((4 − a)/a))^6 =((4/a)−1)^6 =(((3+1)/a)−1)^6 =(((t^3 +1)/( t^2 −t+1))−1)^6 =((((t+1)( t^2 −t+1))/( t^2 −t+1))−1)^6 =(t+1−1)^6 =(t^3 )^2 =3^2 =9

a=93−33+1;(4−aa)6=?let33=t⇒t3=3a=t2−t+1(4−aa)6=(4a−1)6=(3+1a−1)6=(t3+1t2−t+1−1)6=((t+1)(t2−t+1)t2−t+1−1)6=(t+1−1)6=(t3)2=32=9

Answered by A5T last updated on 24/Feb/24

Let p=(3)^(1/3) ; a(p+1)=p^3 +1=4⇒4−a=a(p+1)−a ⇒4−a=ap⇒(((4−a)/a))^6 =p^6 =3^2 =9

Letp=33;a(p+1)=p3+1=4⇒4−a=a(p+1)−a⇒4−a=ap⇒(4−aa)6=p6=32=9

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