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If-x-2-1-3-2-1-3-find-the-value-of-2x-3-6x-

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Question Number 18667 by chernoaguero@gmail.com last updated on 27/Jul/17
If x=2^(1/3) − 2^(−1/3) , find the value of 2x^3 +6x.
Ifx=21/3−2−1/3,findthevalueof2x3+6x.
Answered by ajfour last updated on 27/Jul/17
2x^3 =2[2−3(2^(1/3) −2^(−1/3) )−(1/2)] =3−6x ⇒ 2x^3 +6x=3 .
2x3=2[2−3(21/3−2−1/3)−12]=3−6x⇒2x3+6x=3.
Answered by Arnab Maiti last updated on 27/Jul/17
2x^3 +6x=2(2^(1/3) −2^(−(1/3)) )^3 +6(2^(1/3) −2^((−1)/3) ) =2×[2−3×2^(2/3) ×2^((−1)/3) +3×2^(1/3) ×2^((−2)/3) −2^(−1) ]+6(2^(1/3) −2^((−1)/3) ) =2×[{2−(1/2)}−3{2^(1/3) −2^((−1)/3) }]+6(2^(1/3) −2^((−1)/3) ) =2×{((4−1)/2)}−6×{2^(1/3) −2^((−1)/3) }+6×(2^(1/3) −2^((−1)/3) ) =3
2x3+6x=2(213−2−13)3+6(213−2−13)=2×[2−3×223×2−13+3×213×2−23−2−1]+6(213−2−13)=2×[{2−12}−3{213−2−13}]+6(213−2−13)=2×{4−12}−6×{213−2−13}+6×(213−2−13)=3

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