Question

If a = 3√4 +3√2+1.
Then find the value of (3a^2+3a+1/a^3)^2​

Answer 1

Answer:

Factor the equation to get a(a2+3a+9)=1 , so a2+3a+9=1/a . Thus, 3a=3a2+9a+27 . So we have that a3+3a=a3+3a2+9a+27 . However, by the original equation we have that a3+3a2+9a=1 , so a3+3a2+9a+27=28 , and we are done.

Motivation: The a3+3/a does not look very nice, so you want to isolate the 3/a somehow. This is a common technique in content

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