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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Answer (1)
16th Jan, 2024
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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