Question Number 10193 by konen last updated on 29/Jan/17

x=^3 (√(11+(√(57))))  + ^3 (√(11−(√(57))))  ⇒ x^3 −12x=?

Answered by ridwan balatif last updated on 29/Jan/17

x^3 =(^3 (√(11+(√(57)))) + ^3 (√(11−(√(57)))))^3   x^3 =(^3 (√(11+(√(57)))))^3 +(^3 (√(11−(√(57)))))^3 +3×(^3 (√(11+(√(57)))))(^3 (√(11−(√(57)))))(^3 (√(11+(√(57))))+^3 (√(11−(√(57)))))  remember: (a+b)^3 =a^3 +b^3 +3ab(a+b)  and also remember x=^3 (√(11+(√(57))))+^3 (√(11−(√(57)))),so  x^3 =11+(√(57)) +11−(√(57)) +3×(^3 (√(121−57)))(x)  x^3 =22+3x.(^3 (√(64)))  x^3 =22+12x  x^3 −12x=22