Question
If $x = 3^{1/3}- 3^{-1/3}$, then the value of ($3x^3$ + 9x) is :
Answer: Option A
Answer:(d)$x = (3)^{1/3} - (3)^{-1/3}$On cubing both sides,$x^3 = ((3)^{1/3} - (3)^{-1/3})^3$= $((3)^{1/3})^3-((3)^{-1/3})^3-3×3^{1/3}×3^{-1/3}(3^{1/3}-3^{-1/3})$=$3-3^{-1}-3×x=3-1/3-3x$$x^3 + 3x = 3- 1/3={9- 1}/3$$x^3 + 3x = 8/3$$3x^3 + 9x = 8/3 ×3 =8$
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Answer:(d)$x = (3)^{1/3} - (3)^{-1/3}$On cubing both sides,$x^3 = ((3)^{1/3} - (3)^{-1/3})^3$= $((3)^{1/3})^3-((3)^{-1/3})^3-3×3^{1/3}×3^{-1/3}(3^{1/3}-3^{-1/3})$=$3-3^{-1}-3×x=3-1/3-3x$$x^3 + 3x = 3- 1/3={9- 1}/3$$x^3 + 3x = 8/3$$3x^3 + 9x = 8/3 ×3 =8$
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