Question : If $x=\sqrt[3]{x^{2}+11} –2$, then the value of $(x^3+5x^2+12x)$ is:
Option 1: 0
Option 2: 3
Option 3: 7
Option 4: 11
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Correct Answer: 3
Solution : Given: $x=\sqrt[3]{x^{2}+11} –2$ ⇒ $x+2=\sqrt[3]{x^{2}+11}$ ⇒ $(x+2)^3=(x^{2}+11)$ (Taking cube on both sides) ⇒ $x^3+6x^2+12x+8=x^{2}+11$ ⇒ $x^3+5x^2+12x=3$ Hence, the correct answer is 3.
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