A) \[2{{a}^{3}}\]
B) \[-2{{a}^{3}}\]
C) 1
D) 0
Correct Answer: D
Solution :
Given, \[x={{(a+\sqrt{{{a}^{2}}+{{b}^{2}}})}^{1/3}}+{{(a-\sqrt{{{a}^{2}}+{{b}^{3}}})}^{1/3}}\] On cubing both sides, we get \[{{x}^{3}}=(a+\sqrt{{{a}^{2}}+{{b}^{3}}})+(a-\sqrt{{{a}^{2}}+{{b}^{3}}})\] \[+\,3{{(a+\sqrt{{{a}^{2}}+{{b}^{3}}})}^{1/3}}{{(a-\sqrt{{{a}^{2}}+{{b}^{3}}})}^{1/3}}\] \[\Rightarrow \] \[{{x}^{3}}=2a-3b(x)\] \[\Rightarrow \] \[{{x}^{3}}+3bx-2a=0\]You need to login to perform this action.
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