Problem Solving (PS) | Re: If (3 + 2√2)^(x^2 - 3) + (3 - 2√2)^(x^2 - 3) = b, then which of the fo

OfficialSolution

\( (3 + 2√2)^{(x^2 -3)}\) be y.
(3 + 2√2) and (3 - 2√2) are conjugate numbers.
Since they are conjugate numbers, (3 + 2√2) * (3 - 2√2) = 1
So, (3 + 2√2) =\(\frac{1}{(3−2√2)}\)
or (3 - 2√2) =\(\frac{1}{(3+2√2)}\)
Now,\( (3 - 2√2)^{(x^2 -3)}\) =1/\( (3 + 2√2)^{(x^2 -3)}\) =\(\frac{1}{y}\)

Equation can be writtenas
\( (3 + 2√2)^{(x^2 - 3)} + (3 - 2√2)^{(x^2 -3)}\) = y +\(\frac{1}{y}\) = b
As a rule, the expression: y +\(\frac{ 1}{y}\) ≥ 2 or y +\(\frac{1}{y}\) ≤ -2
From the options, it is clear that y +[m]\frac{1}{y}
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